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text:
You are here: Home / Featured / Response to draft West Sussex Cycling Strategy
Response to draft West Sussex Cycling Strategy
June 20, 2016 by Peter 3 Comments
The Forum has sent the following response to WSCC on the draft Walking and Cycling Strategy.
Support for the work done
We welcome the work done so far in developing a much-needed cycling strategy, in particular:
The development of a mechanism to identify and prioritise schemes for investment.
Recognition of "cycling and walking as a key part of the transport mix".
The support for road space reallocation, segregated tracks alongside fast roads, filtered permeability, cycle contraflows, parking management, speed reduction, together with cycle and walking priority at junctions.
Recognition of the compelling financial and health benefits of investing in cycling.
Recognition of the need to develop more schemes to a stage where they are ready for funding.
Recommendation to adopt as Interim Strategy and continue development
We would like to see this developing work formally recognised by WSCC, but it is vital that this is not seen as 'job done'. We believe that, in order to succeed, the strategy needs further work. We suggest that WSCC adopts the current draft as an "Interim Strategy" with a commitment to continue work on it leading to a complete strategy to be adopted in, say, one year's time.
Clearly this will require continuing officer time – but delivering meaningful change on the ground will require this kind of commitment anyway.
Many local authorities around the country are now starting to reap the benefit of investing in cycling and most of the people who benefit aren't cyclists. Strengthening the strategy now will lead to more effective and efficient delivery over its lifetime.
The reasons we believe that more work is needed on the strategy are explained below.
The objectives are positive but rather vague. For example:
There are no measurable targets either here or under 'Delivery', this reduces the ability to monitor and achieve progress.
The objective to ensure that cycling is "part of" the transport mix is less ambitious than the existing legal requirement within NPPF to give cycling "priority".
One objective should be to implement the strategy by the progressive development of a high quality, safe and comprehensive network of cycle routes suitable for users of all ages and all abilities.
The key factor is leadership
We believe that there is a need to have a single person with the responsibility to lead and deliver the cycling strategy (in contrast to the current proposals for West Sussex to spread responsibility across a number of departments). Recent experience (on the LSTF schemes and with unsuccessful bids for outside funding) indicates that the value gained from this should dwarf the additional overhead cost.
WSCC (like many other local authorities) has previously issued strategies intended to increase cycling but which have had no real effect on the numbers cycling. Local authorities which have succeeded have done so by having a strong leader with a high level of political backing, the responsibility to deliver and the drive to get things done despite inevitable opposition. For WSCC, as a non-unitary authority, there is the additional challenge of also needing to coordinate work with the local planning authorities.
Andrew Gilligan recently looked back on his (strikingly successful) time as 'cycling tsar' in London and said:
"Meaningful cycling schemes almost always have clear majority support, but seldom unanimous support. They will usually inconvenience or upset somebody".
"The key factor is political leadership."
Better infrastructure is needed to achieve real change
There is overwhelming evidence that the key factor which enables cycling is a safe, connected, high quality network that goes where people want to go. The current road conditions deter the majority of people and many of those who would potentially cycle the most (such as children, women and the elderly) tend to be those who are most easily put off by fast and heavy traffic, dangerous junctions, poor surfaces, poor legibility, frequent dismounts, slow and tortuous routes and gaps in the network.
The continuing programme of behavioural change measures can support the strategy, but to achieve a significant and lasting change in the number of people cycling for everyday transport and leisure, there needs to be investment in the infrastructure.
Solely relying on external funding is not enough
External funding specifically for cycling is limited, erratically available and has tended to go to local authorities that have already proven their commitment, have a record of investing in cycling and have a pipeline of projects in development. There are restrictions on where and how developer money (s106 and CIL) can be used. In both cases, match funding is generally needed.
WSCC needs a long-term investment plan for cycling infrastructure
The main continuing internal sources of funding for cycling infrastructure for our roads are likely to be the Highways Infrastructure Block Grant and the Maintenance Block Grant. Currently, the WSCC Highways programmes funded by these grants largely ignore cycling and, as a result, many of the schemes WSCC is actively developing have the effect of making our roads increasingly hostile to cycling. Unless there is a serious commitment to actively provide for cycling within the mainstream budgets, we will be going backwards.
The Government has said that local authorities should use the block grants for cycling and walking. From 2018, 9% of the Maintenance Grant will depend on the amount of cycling infrastructure and footway in the county. The Government's Cycling and Walking Investment Strategy (CWIS) refers to 'typical' capital spending on cycling of 11% of the Integrated Block Grant (plus a further 4% for walking).
In addition cycling infrastructure can be funded through the Local Growth Fund settlement as an integral part of growth schemes as well as via specific 'sustainable transport' pots. The latest Local Growth Fund settlement specifically includes (non-ring fenced) money for this.
Due to the potential public health benefits to be gained from increasing cycle journeys a proportion of the Public Health Department budgets could also be allocated to cycle infrastructure projects as has been done elsewhere in the country.
This February Robert Goodwill, Minister for Cycling in the DfT said "We need to trust the people in the local enterprise partnerships, local authorities and combined authorities to understand the importance of cycling… Long-term funding will be available from a wide range of sources, including the new access fund, the integrated transport block, the highways maintenance block and the local growth fund. That means that everywhere that wishes to invest £10 per head will be able to."
Although we recognise that funding is squeezed, tighter budgets should logically lead to a higher proportion of expenditure on cycling schemes as they typically have higher benefit to cost ratios than existing roads projects.
Cycling infrastructure, even for 'flagship' schemes, is much cheaper than general roads infrastructure. Ironically, a persistent problem in UK authorities which have invested in cycling has been underspending of budgets (because it takes time to develop the technical and political capability to deliver). Relatively small initial budgets spent on meaningful projects could make significant improvements whilst building the capacity to deliver in the future.
If cycling investment is not considered important enough to be included as an integral part of the highways budget with a percentage of the capital and maintenance budgets specifically allocated for it, then there is doubt as to whether there is the political commitment required to back the whole strategy.
Current issues in delivery capability need to be addressed
The draft speaks of the LSTF cycling project as though it was a success whereas substantial sums of money were spent on interventions which almost entirely failed to deliver benefits to people who wish to cycle.
Other current projects (locally, for example, the Parsonage Road cycle lanes and the Broadbridge Heath Leisure Centre) continue to show that the existing planning process does not deliver adequate cycling infrastructure.
Without acknowledging and understanding these problems and making the necessary changes to internal processes, future schemes will suffer a similar fate. Members of the Horsham forum are willing to meet officers or members to provide more information about the issues we have observed and which cause us concern.
There has been, and continues to be, rapid change in engineering regulation, guidance and best practice. The strategy should address the need for access to up-to-date technical experience and expertise (through training, recruitment of staff with the necessary skills and use of specialist consultants) and also ensure that it is more proactive in its support for local planning authorities which no longer have their own in-house expertise and therefore rely very heavily on WSCC (as the highways authority) to guide them.
We wish to see WSCC making active use of the maintenance programme to make cost-effective improvements to cycling infrastructure as a part of scheduled work.
West Sussex needs best practice design
We would like to see the strategy go beyond simply referring to DMRB (Design Manual for Roads and Bridges, which is for trunk roads and is not always appropriate for local roads) and Manual for Streets, and also make specific reference to the best recent guidance including the London Cycling Design Standards, and the recent changes in TSRGD (Traffic Signs Regulations and General Direction, 2016) which now include cycle zebras permitting the construction of roundabouts with segregated tracks.
Since best practice is evolving rapidly we would also like to see encouragement given to designers to take advantage of ongoing improved designs in the UK and, where appropriate, overseas. For example, the Government Cycle Proofing Working Group has been set up to assist and has started to publish a list of case studies.
In West Sussex as elsewhere money has been spent on cycling infrastructure which is barely used because it does not offer real improvements to safety or convenience. We would like WSCC to follow the lead given by London in adopting a policy where:
"Timid, half-hearted improvements are out – we will do things at least adequately, or not at all."
The draft strategy promotes shared space for cyclists and pedestrians. There needs to be greater clarity that this is only an acceptable solution where speeds and volumes of users are low (for example some rural routes, where there are few users, or home zones and pedestrianised areas where speeds are very low). In other situations sharing space is a poor solution for both user groups. Shared use footways are generally too narrow, with poor visibility at driveways and corners; users are required to give way at every minor exit and the surfaces are uneven with sloping driveways.
Outside of built-up areas or on public rights of way, the strategy is still based on providing unsealed (gravel) tracks for cycling. These deteriorate quickly, especially in the absence of maintenance and are not suitable for year-round commuting or utility trips where people cycle in everyday clothes and don't want to arrive covered in mud. Sustrans advice is that sealed (tarmac) surfaces not only give a better riding experience, but cost less in the long run and are preferred, even for off-road general leisure routes. We would like to see the strategy adopt a presumption in favour of sealed surfaces on utility and high-use general leisure cycling routes.
Route prioritisation
The strategy prioritises inter-community utility routes. These routes are certainly important but it seems they are prioritised here largely because they are seen as the projects which are most likely to win current specific pots of money from the Coast to Capital LEP rather than because of taking a wider view of needs.
The majority of potential cycling trips are day to day short trips to school, work, shops and leisure activities, particularly in built-up areas. The strategy needs to place more emphasis on this kind of everyday transport cycling and the infrastructure needed to make it a realistic choice for 'ordinary people' who (far more than sports cyclists) are currently put off cycling because of the road conditions.
Although individual projects are likely to focus on "individual routes", the strategy needs to be based around the progressive development of a coherent network of routes. This may mean that investment should initially be concentrated around a limited number of key locations to maximise impact – even though this will mean difficult political choices when one area is favoured over another.
Because there is very little supporting information for many of the routes in the RATE process, the true rankings could change significantly as more information is added. It is therefore important that there is further discussion and input from stakeholders before initial routes are selected for feasibility studies.
We would like to see more detail ensuring that the RATE list is maintained, updated and actively incorporated in the planning and other processes.
Lack of priority for new developments
A glaring omission in the draft strategy is a clear plan to ensure that all new developments incorporate appropriate layouts and high quality cycling infrastructure (including off-site improvements to overcome severance and to enable cycling to local shops, schools and services).
Routes for new developments are not adequately prioritised in the RATE list – for example cycling within the north of Horsham development and the routes connecting to it are not given high priority, which means there is a real risk that we will continue to build and lock in out-dated design for decades to come.
There are major housing developments taking place across West Sussex; this is a huge opportunity to design for cycling and walking with a significant proportion of the funding coming from the developers. Planning for good provision for walking and cycling from does not necessarily have a large impact on developers' total costs and can help increase the attractiveness of developments. In order to achieve good design and maximise the benefit from s106 and CIL contributions WSCC needs to give stronger and clearer guidance to developers and to provide a higher level of support to local planning authorities and neighbourhood planning groups. Further development of the draft strategy could be part of this, as could help to develop local policies on cycling via supplementary planning documents (SPDs).
Better cycle parking standards are needed
The strategy should include a plan to review cycle parking strategy in the county. The current WSCC guidance has numerical standards for cycle parking (which are a useful tool in the planning process) but has little to say about design standards for cycle parking. This leads to new housing largely providing cycle parking in garages or back garden sheds, which is often inadequate and inaccessible.
The strategy should include an action to review current guidance on residential, commercial and public cycle parking to include design guidance for developers, based on the principle that "cycle parking should be at least as convenient as car parking".
This would mean secure, covered cycle parking at the front of homes, step-free internal access to cycle parking for flats, on-street lockable cycle hangars, convenient space for visitor parking and provision for non-standard cycles including tandems and cargo bikes and mobility buggies. For shops, offices and public places, cycle parking should be as close as possible to the entrance, covered and well-overlooked. Good example documents include Cycle Parking Guide for New Residential Developments by Cambridge City Council, the LCDS and a briefing note from the Horsham forum.
Speed reduction and roads policing
The strategy mentions speed reduction, but underestimates its importance (in both urban and rural situations). There should be a plan to review the existing policy on speed limits and zones with a particular focus on improving safety for people cycling and walking.
We also wish to see WSCC working with the Sussex Safer Roads Partnership to increase enforcement against the kinds of poor driving which put people on bikes at particular risk, for example: close overtakes, use of mobile devices and aggressive driving.
Economic benefits for town centres
We propose that one objective of the strategy should be to work with districts across the county to develop schemes aimed at attracting more people to cycle to local town and village centres.
There is now strong evidence that increasing levels of cycling has a significant benefit to the local economy. The recent DfT commissioned report 'The Value of Cycling' found the following:
Cyclists visit local shops more regularly, spending more than users of most other modes of transport.
Per square metre, cycle parking delivers 5 times higher retail spend than the same area of car parking.
A compact town optimised for walking and cycling can have a "retail density" (spend per square metre) 2.5 times higher than a typical urban centre.
Public realm improvements, including those that cater for cycling, have been shown to result in increased trade at local businesses.
As a cycle forum, we support the position of pedestrians at the top of the hierarchy of users and feel there is a case for a stronger pedestrian element (with especial consideration to the more vulnerable and those with disabilities) within the strategy.
One area where pedestrian and cycling interests overlap strongly is limiting vehicle access in residential areas to prevent rat-running. This type of 'filtered permeability' scheme tends to be very popular once implemented and many, probably the majority, of the benefits (quieter, less polluted, safer streets with more space for walking, playing and social interaction) are to people who do not cycle. However, initial introduction of new schemes can be contentious so it is important to work to gain active support from the wider community, not just existing cyclists.
Presentation of the strategy
We think that including more photographs will help demonstrate the aspirations of the strategy and improve understanding and communication with local planning authorities, contractors and developers. We are happy to help provide some photographs.
Photographs could include:
People old and young using bikes, disability adapted cycles, e-bikes, cargo bikes, child-carrying bikes and also mobility scooters.
People cycling to work, school, the shops and leisure activities in everyday clothes without the need for hi vis and protective clothing.
Independent trips by children, people having fun, cycling at a leisurely pace with enjoyment and social interaction
Examples of excellent cycling infrastructure including cycleways alongside main roads; filtering to create quiet streets for residents and for walking and cycling, smooth, sealed off-road leisure routes; busy junctions with protection for cycling; cycle contraflows; cycle-priority crossings (cycle-zebras) and cycle phases on traffic signals; continuous foot and cycleways across side roads; exemplary cycle parking for homes and destinations; space for cycling replacing parking to improve access to town centre shops etc.
Similarly, we would like to see a clear summary of the economic, health and social benefits for investing in cycling. See for example Benefits of Investing in Cycling and The Value of Cycling.
HDCF, 20 June 2016
Michael Gimber says
The RATE tables seem to have a certain amount of duplication. I hope the first task is to reduce this confusing duplication.
geoffrey bragg says
I support Horsham District Cycle Forums excellent response to the Draft West Sussex Cycling and Walking Stratagy.It would seem to me that the only way that the County Council will ever achieve even an"adequate"Cycle and Walking Strategy is to have a single officer expert in his field with responsibilty to lead and deliver the Strategy against the inevitable opposition.To do otherwise is going to lead to more inefficient use of public funds and lost opportunities and in so doing let down future generations for years to come.
Anthony Cartmell says
An excellent response to the draft Walking and Cycling Strategy document, that I fully support.
The question is, do WSCC really want to improve conditions for people using bicycles for transport, or is the Walking and Cycling Strategy document designed to be ignored? Is there a genuine wish to invest in sustainable transport, or is the whole process just "going through the motions"?

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\section{Introduction}
It is widely recognized that an accurate description of the dynamics of
holes in antiferromagnetically (AF) ordered materials is an important
first step towards an understanding of the essential physics of the cuprate
superconductors.
Consequently, numerous investigations
\cite{Dagotto94,Tohyama96,Xiang96,Hayn96,Sheng96,Vojta96,Brinkman70,Trugman90,%
Li89,Pecher95,Shankar90,Wiegmann88}
have dealt with the problem of a single hole in a square-lattice
antiferromagnet.
Most of these studies are based on an effective Hamiltonian ${\cal H}_{\Box}$
\cite{Kane89,Marsiglio91} which describes the hole as a spinless fermion
which is coupled to bosons representing the collective excitations (magnons)
of the antiferromagnetic background.
The structure of this effective Hamiltonian reflects the two-sublattice
structure of the square lattice AF.
When the hole hops between nearest neighbour lattice sites, it necessarily
disturbs the magnetic order.
Thus, any move of the hole requires absorption or emission of a magnon.
Derivations of ${\cal H}_{\Box}$ from the t-J Hamiltonian have revealed
the approximate nature of this effective Hamiltonian \cite{Barentzen94},
and to obtain the spectrum of a hole from ${\cal H}_{\Box}$
further approximations are necessary.
Most often, the fermion-magnon coupling is treated in the self-consistent
Born approximation (SCBA) which was already used in the original studies
by Kane et al. \cite{Kane89} and Marsiglio et al. \cite{Marsiglio91}.
Surprisingly, the approximate spectra obtained in this manner agree excellently
with the spectra of small clusters obtained by numerically exact
diagonalization of the $t-J$ Hamiltonian for these clusters.

Apart from its relevance to the physics of cuprate superconductors, the
dynamics of holes in ordered antiferromagnets is a highly nontrivial
problem of the physics of strongly correlated electron systems, and it is
therefore of fundamental theoretical interest. Here, we shall present
a derivation of effective Hamiltonians for holes in AFs which is not
restricted to any particular type of magnetic order. Our method does not
provide us with a unique effective Hamiltonian for an arbitrary number of
holes. Rather the cases of a single hole, two holes and in general an
arbitrary but fixed number of holes have to be treated separately. While
our presentation remains general, we shall confine ourselves to the
single-hole problem in order to demonstrate our method's practical
applicability. In
particular, we shall derive and evaluate the effective Hamiltonian
${\cal H}_{\triangle}$ for a single hole in the triangular AF.

\section{Effective Lagrangian}
For definiteness, we consider the $t-J$ Hamiltonian,
\begin{eqnarray}
{\cal H}&=& -t \sum_{\stackrel {<{\bf r},{\bf r'}>}{\sigma}}
\hat{P} (c_{{\bf r},\sigma}^{\dagger} c_{{\bf r'},\sigma}^{} + {\it h.c.})
\hat{P} \nonumber\\
&&+J\sum_{<{\bf r},{\bf r'}>} \hat{\bf S}_{\bf r}\cdot \hat{\bf S}_{\bf r'}\, .
\label{t-J}
\end{eqnarray}
$t$ and $J$ are the single particle hopping matrix element and the exchange
constant, respectively, the operator $\hat{P}$ projects onto states in which
each of the $N_s$ lattice sites is either empty or singly occupied, and
$\hat{\bf S}_{\bf r}=\frac{1}{2} c_{{\bf r},\alpha}^{\dagger}
\mbox{\boldmath $\sigma$}_{\alpha,\beta} c_{{\bf r},\beta}^{}$
is the electron spin expressed in terms of creation and annihilation operators,
$c^{\dagger}_{{\bf r},\alpha}$ and $c^{}_{{\bf r},\alpha}$,
for fermion states at site ${\bf r}$ with spin projection $\alpha$.
The sums in (\ref{t-J}) run over pairs $<\, , \,>$ of nearest neighbour sites
of the lattice.

In order to cast the partition function ${\cal Z}={\it tr}\exp\{-\beta
{\cal H}\}$ into the form of a path integral, we introduce the following coherent states \cite{Wiegmann88}
for each lattice site ${\bf r}$ (we omit the site index wherever this does not
lead to ambiguities):
\begin{eqnarray}
|\omega\!>&=&e^{\left[\eta c-c^{\dagger}\eta^*\right]} |\Omega\!>,\nonumber\\
|\Omega\!>&=&c^{\dagger} |0\!>, \nonumber\\
 c^{\dagger}&=&
 e^{-i\phi/2}\cos\frac{\theta}{2} e^{-i\psi/2}c_{\uparrow}^{\dagger}
+e^{ i\phi/2}\sin\frac{\theta}{2} e^{-i\psi/2}c_{\downarrow}^{\dagger}.
\label{coh}
\end{eqnarray}
Here, $\eta$, $\eta^*$ are Grassmann variables, and $|0\!>$ is the vacuum
with no spins present.
Obviously, $|\Omega\!>$ is a one-fermion state with spin in the direction
$(\theta,\phi)$ on the sphere.
The inclusion of a phase factor which depends on the third Euler angle $\psi$
is necessary, if $|\Omega\!>$ and $\eta$ are to satisfy the following
requirements: ({\it i}) $|\Omega\!>$ is to transform covariantly under
{\it all} $SU(2)$ operations, while ({\it ii}) $\eta$ remains invariant
under these operations.
As will be seen shortly, both requirements appear natural in view of
the physical interpretation of the variables $\Omega=(\psi,\theta,\phi)$
and $\eta$.
It is easily checked that the states $|\omega\!>$ {\it include}
the empty and the spin-up and spin-down states of the fermion, but {\it
exclude} the doubly occupied state. In fact, the states $|\omega\!>$ are
complete in this three-dimensional space,
\begin{eqnarray}
&&\int d\omega\, |\omega\!><\!\omega|:=\nonumber\\
&& \int d\Omega\,\frac{1}{2}\int d\eta^{*} d\eta\,
e^{-\eta^{*}\eta}|\omega\!><\!\omega|=\nonumber\\
&&\int d\Omega\,\frac{1}{2}\int d\eta^{*} d\eta\,e^{-2\eta^{*}\eta}
\left\{\eta \,\eta^* |0\!><\!0|+|\Omega\!><\!\Omega|\,\right\}\nonumber\\
&&={\bf 1}_3
\label{comp}
\end{eqnarray}
where $\int d\Omega \cdots = \frac{1}{8\pi^2} \int_{0}^{4\pi}d\psi
\int_{0}^{\pi}d\theta \sin{\theta} \int_{0}^{2\pi}d\phi \cdots$.
The Euler angles $\Omega$ describe the spin degrees of freedom and the
Grassmann variables $\eta$ and $\eta^{*}$ a spinless fermionic hole.
Thus the requirement ({\it ii}) is cogent.
With these coherent states, the standard steps towards a path integral
representation of the partition function yield
\begin{eqnarray}
{\cal Z}_M&=&\int {\cal D}_M[\Omega]\int {\cal D}_M[\eta^*,\eta^{}]\nonumber\\
&&\prod_{\stackrel{\tau=1}{{\bf r}}}^M
\left(<\!\Omega_{\tau-1,{\bf r}}|\Omega_{\tau,{\bf r}}\!>\frac{1}{2}
e^{-2\eta_{\tau,{\bf r}}^{*}\eta_{\tau,{\bf r}}^{}}\right)\nonumber\\
&& \exp\left\{\sum_{\tau,{\bf r}} \frac{\eta_{\tau-1,{\bf r}}^*\eta_{\tau,{\bf
r}}^{}}{<\!\Omega_{\tau-1,{\bf r}}|\Omega_{\tau,{\bf r}}\!>} +
\right.\nonumber\\
&& \left. \sum_{\tau}
\ln\left[1+\frac{<\!\omega_{\tau-1}| e^{-\Delta\tau {\cal H}} -
1|\omega_{\tau}\!>}{<\!\omega_{\tau-1}|\omega_{\tau}\!>} \right]\right\},
\label{Z}
\end{eqnarray}
with ${\cal D}_M[\Omega]=\prod_{\tau=1,{\bf r}}^M d\Omega_{\tau,{\bf r}}$ and
${\cal D}_M[\eta^*,\eta]=\prod_{\tau=1,{\bf r}}^M d\eta^{*}_{\tau,{\bf r}}d\eta^{}_{\tau,{\bf r}}$.
Here, sums and products run over the $M$ (imaginary) time slices of the Trotter
decomposition of $\exp(-\beta {\cal H})$ (subscript $\tau$) and over the $N_s$
lattice sites (subscript ${\bf r}$).
$\Delta\tau=\beta/M$ is the width of the time slices.
The boundary conditions are $\Omega_{0,{\bf r}}=\Omega_{M,{\bf r}}$ and
$\eta^{(*)}_{0,{\bf r}}=-\eta^{(*)}_{M,{\bf r}}$.
The final step in the conversion of ${\cal Z}_M$ into a path integral would be
to take the continuum limit $M \rightarrow \infty$ in the time direction.
This meets with difficulties.
After the expansion of the second exponential in (\ref{Z}) to linear order in
$\Delta\tau$, a factor
$\prod_{\tau,{\bf r}}e^{-\eta_{\tau,{\bf r}}^*\eta_{\tau,{\bf r}}^{}}$
remains in the integrand which is therefore {\it ill} defined in the limit
$M\rightarrow \infty$. However, as we shall show now, the individual
summands ${\cal Z}^{n-hole}$ in the decomposition
\begin{equation}
{\cal Z}_M=
{\cal Z}_{M}^{0-hole}+{\cal Z}_{M}^{1-hole}+\ldots+{\cal Z}_{M}^{n-hole}+\ldots
\label{dec}
\end{equation}
of the partition function ${\cal Z}_M$ into
$0$-, $1$-, $\ldots n$-hole contributions are {\it well} defined in the
$\tau$-continuum limit. Since in this work we are interested in the
one-hole effective Hamiltonian, which can be extracted from ${\cal Z}^{1-hole}$,
we confine our attention to the first two terms of (\ref{dec}).
The crucial elements in this decomposition are the weight factors
$e^{-2\eta_{\tau,{\bf r}}^{*}\eta^{}_{\tau,{\bf r}}}
=1-2\eta^{*}_{\tau,{\bf r}} \eta^{}_{\tau,{\bf r}}$
in the integrand of (\ref{Z}). From (\ref{comp}) it follows that
the identity in such a factor projects onto configurations with a hole at
$(\tau,{\bf r})$ while the second term, $-2\,\eta^{*}_{\tau,{\bf r}} \eta^{}_{\tau,{\bf r}}$, projects onto
configurations with an electron at $(\tau,{\bf r})$. Thus, by retaining in
the integrand of (\ref{Z}) only the term
$\prod_{\tau,{\bf r}}\left(-2\eta^{*}_{\tau,{\bf r}}\eta^{}_{\tau,{\bf r}}\right)$
of the expansion of
$\prod_{\tau,{\bf r}}\left(1-2\eta^{*}_{\tau,{\bf r}}\eta^{}_{\tau,{\bf r}}\right)$,
one obtains ${\cal Z}^{0-hole}$, the partition function with no hole at all
which is, of course, the partition function of the Heisenberg Hamiltonian.
Similarly, by retaining those terms of the expansion which contain for each
time slice $\tau$ just $N_s-1$ factors
$-2\eta^*_{\tau,{\bf r}}\eta^{}_{\tau,{\bf r}}$ one obtains
${\cal Z}^{1-hole}_M$.
(The number of holes remains constant in time.)
Using the identity
\begin{equation}
\prod_{\tau,{\bf r}} \left. \left( \frac{1}{2} e^{-2\eta_{\tau,{\bf r}}^{*}
\eta^{}_{\tau,{\bf r}}} \right) \right|_{1-hole} =
\frac{1}{2^M} \prod_{\tau,{\bf r}} \left. \left( e^{- \eta^{*}_{\tau,{\bf
r}} \eta^{}_{\tau,{\bf r}}} \right) \right|_{1-hole},
\end{equation}
which holds between the one-hole projectors on both sides,
we can now cast ${\cal Z}^{1-hole}_M$ into the form
\begin{eqnarray}
{\cal Z}^{1-hole}_M&=&
\frac{1}{2^M} \int{\cal D}_M[\Omega] \int{\cal D}_M[\eta^*,\eta]\nonumber\\
&&\prod_{\stackrel{\tau=1}{{\bf r}}}^M
\left(<\!\Omega_{\tau-1,{\bf r}}|\Omega_{\tau,{\bf r}}\!> \right)\nonumber\\
&&\exp\left\{-\sum_{\tau,{\bf r}} \left(\eta_{\tau,{\bf r}}^*\eta_{\tau,{\bf r}}^{}-
\frac{\eta_{\tau-1,{\bf r}}^*\eta_{\tau,{\bf r}}^{}}{<\!\Omega_{\tau-1,{\bf r}}|
\Omega_{\tau,{\bf r}}\!>}\right)\right. + \nonumber\\
&& \,\, \left. \left.\sum_{\tau}
\ln\left[1+\frac{<\!\omega_{\tau-1}| e^{-\Delta\tau {\cal H}} -
1|\omega_{\tau}\!>}{<\!\omega_{\tau-1}|\omega_{\tau}\!>}
\right]\right\}\right|_{1-hole}\!\!\!\!\!.\nonumber\\
\label{ZH1M}
\end{eqnarray}
The additional factor of $\frac{1}{2}$ associated with each time slice
$\tau$ finds a natural explanation:
It compensates for the integrations over the redundant spin variable at the
position of the hole \cite{MacDonald97}.
Obviously, the integrand of (\ref{ZH1M}) is well defined in the
$\tau$-continuum limit $M \rightarrow \infty$. Performing this limit, one obtains
\begin{equation}
{\cal Z}^{1-hole}\,\,
=\,\,\left.\int {\cal D}[\Omega]\int {\cal D}[\eta^{*},\eta]\,\,
e^{\,\int^{\beta}_0 d\tau {\cal L}}\right|_{1-hole}
\label{ZH1}
\end{equation}
with the classical Lagrangian for one hole
\begin{eqnarray}
{\cal L}&=&\sum_{\bf r}\left[1-
\eta_{\bf r}^{*}(\tau)\eta_{\bf r}^{}(\tau)\right]<\!\Omega_{\bf r}(\tau)|
\dot{\Omega}_{\bf r}(\tau)\!> \nonumber\\
&&+\sum_{\bf r} \eta^{*}_{\bf r}(\tau) \dot{\eta}_{\bf r}^{}(\tau)
\,-\,<\omega(\tau)|{\cal H}|\omega(\tau)>_{1-hole}.
\label{LH1}
\end{eqnarray}
Here, $|\omega(\tau)\!>=\prod_{\bf r}|\omega_{\bf r}(\tau)\!>$, and
$<\omega(\tau)|{\cal H}|\omega(\tau)>_{1-hole}$ denotes that part of the
expectation value which is bilinear in the Grassmann fields $\eta^{*},\eta$.

It should be clear from these considerations that in order to determine the
effective interaction between a pair of holes, one will have to analyze the
2-hole contribution to ${\cal Z}_M$. In calculating it from the 1-hole
contribution by integrating over the spin degrees of freedom, one would miss a
part of this interaction.

Evaluating (\ref{LH1}) with the states (\ref{coh}) and the Hamiltonian
(\ref{t-J}) of the $t-J$ model on an arbitrary lattice,
we obtain ${\cal L}= {\cal L}_{kin}+{\cal L}_t+{\cal L}_J$, where
(we omit total time derivatives)
\begin{eqnarray}
&&{\cal L}_{kin}=\sum_{\bf r} \left[\eta^*_{\bf r} \dot{\eta}^{}_{\bf r}
+\frac{i}{2}\eta^*_{\bf r}\eta^{}_{\bf r}\dot{\psi}^{}_{\bf r}\right.\nonumber\\
&&\qquad\qquad-\left.\frac{i}{2}\left(1-\eta^{*}_{\bf r}\eta^{}_{\bf r}\right)
\dot{\phi}_{\bf r}\cos(\theta_{\bf r})\right] \; ,
\label{Lkin}
\end{eqnarray}
\begin{eqnarray}
&&{\cal L}_t=-t \,\sum_{<{\bf r,r'}>}\left\{\eta^*_{\bf r'}\eta^{}_{\bf r}
     e^{-\frac{i}{2}(\psi_{\bf r'}-\psi_{\bf r}^{})}\right.\nonumber\\
&&\left[ \cos\left(\frac{\phi_{\bf r}-\phi_{\bf r'}}{2}\right)
       \cos\left(\frac{\theta_{\bf r}-\theta_{\bf r'}}{2}\right)\right.
\nonumber\\
&&\left.\left.+\,\,i\sin\left(\frac{\phi_{\bf r}-\phi_{\bf r'}}{2}\right)
       \cos\left(\frac{\theta_{\bf r}+\theta_{\bf r'}}{2}\right)\right]\,
        +\,({\bf r}\leftrightarrow {\bf r'}) \right\}
\end{eqnarray}
and
\begin{equation}
{\cal L}_J=-J\sum_{<{\bf r,r'}>}(1-\eta^{*}_{\bf r}\eta^{}_{\bf r}\,\, -\,\, \eta^{*}_{\bf r'}\eta^{}_{\bf r'})\;
{\bf S}_{\bf r}\cdot{\bf S}_{\bf r'} \; .
\label{Lj}
\end{equation}
The Heisenberg term ${\cal L}_J$ accounts for the interaction between spins
${\bf S}=\frac{1}{2} (\sin\theta \cos\phi, \sin\theta \sin\phi,\cos\theta )$
at sites where no hole is present.
${\cal L}_t$ describes the hopping of the hole; the hopping energy depends
on the state of the spins.
Finally, ${\cal L}_{kin}$ contains the kinetic terms of a spinless hole
($\eta^{*}\dot{\eta}$), and a spin $\frac{1}{2}$, i.e. $\dot{\phi}\cos(\theta)$.
In addition, two terms couple the hole to the angular degrees of freedom.
The second cancels the kinetic term of the spin at sites where a hole is
present.
The first has the form of a gauge interaction with the field $\psi$.
It is tempting to use a parameterization in which the factor
$\exp(\frac{i}{2}\psi)$ is absorbed in $\eta$, since then, all the $\psi$
dependent terms in ${\cal L}$ disappear.
However, after such a gauge transformation, $\eta$ is no longer invariant
under $SU(2)$ operations, as explained above in connection with the choice
of the coherent states (\ref{coh}).
Since this has unwanted consequences, we do not follow this route.

In summary, our procedure for obtaining effective Hamiltonians consists of
the following steps:
first we represent the partition function of the initial quantum Hamiltonian
as a discrete-time path integral; then, we identify that part of the partition
function that corresponds to the number of holes we wish to consider; in this
part, we then perform the continuum limit to obtain the classical Lagrangian;
finally, we translate back to an effective quantum Hamiltonian.

The Lagrangian ${\cal L}$, (\ref{Lkin}-\ref{Lj}), still represents the full
non-linear problem of a hole interacting with the spin background. In the
following, we shall confine ourselves to a spin wave expansion around the
classical spin groundstate of ${\cal L}$.
In this picture, the hole moves in a spin background described by angular fields
which deviate little from their groundstate. The spin wave expansions have, of
course, to be performed separately for the case of collinear spin order (square
lattice AF) and for the case of planar spin order (triangular lattice AF).
We shall briefly rederive the quantum Hamiltonian, ${\cal H}_{\Box}$, which is
well known for the case of collinear spin order. For the case of planar spin
order, we obtain a significantly different effective Hamiltonian
${\cal H}_{\triangle}$. To
check the validity of the approximations that lead to ${\cal H}_{\triangle}$
we shall calculate the one hole spectral properties that follow from
${\cal H}_{\triangle}$ and compare them with results obtained by numerically
exact diagonalization of the $t-J$ model for small finite lattice cells.

\section{One hole on a square lattice}
The two sublattice classical AF order is reproduced by assigning the value
$\pi/2$ to $\theta_{\bf r}$ and the values $\phi_{\bf r}^{(0)}=\pm\pi/2$ to
$\phi_{\bf r}$ for ${\bf r}$ from the A or B lattice, respectively.
The deviations from the ordered groundstate, $x_{\bf r}$ and $p_{\bf r}$
defined by
\begin{equation}
 \phi^{}_{\bf r}=\phi^{(0)}_{\bf r}+ \sqrt{2}x_{\bf r} \mbox{\hspace{1cm}}
\theta_{\bf r}=\frac{\pi}{2}+\sqrt{2} p_{\bf r} \;,
\label{coorsq}
\end{equation}
are canonically conjugate harmonic oscillator fields as can be seen from
${\cal L}_{kin}$.
Now, we expand ${\cal L}$ up to quadratic order in the amplitudes
$a=(x-ip)/\sqrt{2}$ and $a^*$
and keep in the quadratic term only the leading zero--hole contribution.
Then, the spin and the hole degrees of freedom decouple in ${\cal L}_{kin}$.
We redefine the hole field by
$h\,\equiv\,\eta\,e^{\frac{i}{2}(\psi - \phi^{(0)})}$.
Then, all the phases in the hopping term in the path integral become equal;
the field $\psi$ disappears from ${\cal L}$ and is integrated out.
Finally, we translate back to operator form and get
\begin{eqnarray}
 {\cal H}_{\Box}&=&-t\sum_{<\!{\bf r}, {\bf r'}\!>}
 \left[h^{\dagger}_{\bf r'}h^{}_{\bf r} \, i \,
 \left(a^{\dagger}_{\bf r}-a^{}_{\bf r'}\right)+h.c.\right] \nonumber\\
&&+\frac{J}{2} \sum_{<\!{\bf r}, {\bf r'}\!>}
 \left(a^{\dagger}_{\bf r}a^{}_{\bf r} +a^{\dagger}_{\bf r'}a^{}_{\bf r'}
  -a^{\dagger}_{\bf r}a^{\dagger}_{\bf r'}-a^{}_{\bf r'}a^{}_{\bf r}\right)
\nonumber\\
&&+J \sum_{\bf r} \left(h^{\dagger}_{\bf r}h^{}_{\bf r}-\frac{1}{2}\right).
\end{eqnarray}
${\cal H}_{\Box}$ is, up to a canonical transformation
($a_{\bf r} \rightarrow - i a_{\bf r}$) identical with the Hamiltonian
considered in \cite{Marsiglio91}.
The last term in ${\cal H}_{\Box}$, containing the hole number,
accounts for the breaking of four bonds per hole in the classical groundstate.

\section{One hole in the triangular lattice}
In the classical limit, the groundstate of the $t-J$ model at half filling is
the well known planar ${120}^{\small o}$ spin structure:
$\theta^{(0)}_{\bf r}=\pi/2$ for all
${\bf r}$ and $\phi^{(0)}_{\bf r}=\frac{2\pi}{3},0,-\frac{2\pi}{3}$ for
the A, B and C sublattice, respectively.
As in the case of the square lattice, we describe the deviations from this
ordered groundstate by the spin wave amplitudes $x_{\bf r}$ and $p_{\bf r}$
which are canonically conjugate harmonic oscillator fields.

Proceeding as in the square lattice case, i.e. expanding to second order
in the amplitudes $a$ and $a^*$ and integrating over $\psi$, one would be left
with terms in ${\cal L}_t$ that couple the hole motion to zero energy spin modes.
But these modes are uniform spin rotations which are exact symmetries
of the initial model (\ref{t-J}). Therefore, they cannot appear in any order
of a perturbation expansion.
In the Appendix, we trace this apparent inconsistency back to the integration
over the field $\psi$.
We show how to derive a result which is free of zero modes, as it should be,
and we explain why the same difficulty does not occur in the case of the square
lattice.
Retaining terms of the same order in the amplitudes $a$, $a^{*}$ as in the
square lattice case, we find the following effective Hamiltonian
for one hole in the triangular AF (in momentum space)
\begin{eqnarray}
{\cal H}_{\triangle}&=&\frac{3J}{4}\sum_{\bf q}\left\{
(2+w_{\bf q})a^{\dagger}_{\bf q}a^{}_{\bf q}
-\frac{3w_{\bf q}}{2}(a^{\dagger}_{-{\bf q}}a^{\dagger}_{\bf q}
+a^{}_{-{\bf q}}a^{}_{\bf q})\right\}   \nonumber\\
&&-\frac{3JN_s}{8}+\sum_{\bf q}\epsilon_{\bf q} \;h^{\dagger}_{\bf q}h^{}_{\bf q}
    \nonumber \\
&& +\frac{1}{\sqrt{N_s}}\sum_{\bf q,q'}\left\{ f_{\bf q,q'} \;
 h^{\dagger}_{\bf q} h^{}_{\bf q'} \;a_{\bf q-q'} + h.c. \right\} \; .
\label{H3}
\end{eqnarray}
The terms in the first line are nothing but the linear spin wave approximation
(LSW) of the triangular Heisenberg AF. The last line contains the coupling between the hole and the magnons with the hole-magnon vertex
\begin{eqnarray}
f_{\bf q,q'}&=&
  3 \sqrt{3} i \left[ -t\gamma_{\bf q'}+\frac{J}{4}\gamma_{\bf q-q'} \right]
\nonumber \\
&& + \sqrt{3} \left(\frac{1}{2}+w_{\bf q-q'}-i\gamma_{\bf q-q'}\right)
\times\nonumber\\
&&\left[ t (w_{\bf q}-w_{\bf q'}) + \frac{J}{2} (1-w_{\bf q-q'}) \right] \; .
\end{eqnarray}
Here, $w_{\bf q}$ is defined by
\begin{equation}
w_{\bf q}+i\gamma_{\bf q}=
\frac{1}{3} \sum^3_{j=1} e^{i{\bf q} \cdot \mbox{\boldmath $\scriptstyle \delta$}_j}
\end{equation}
and $\mbox{\boldmath $\delta$}_j = (\cos \varphi_j, \sin \varphi_j)$,
$\varphi_j = \frac{2\pi}{3}j$, are the vectors to the three nearest neighbour
sites on the triangular lattice.
As opposed to the square lattice, the hole can hop on the triangular lattice
without emission or absorption of a magnon. This is expressed by the second
line of (\ref{H3}) where
\begin{equation}
\epsilon_{\bf q} = \frac{3J}{4}-3tw_{\bf q} \; ,
\end{equation}
is just half the dispersion of a particle hopping between nearest neighbour
sites of the empty triangular lattice.
${\cal H}_{\triangle}$ constitutes our main result for the Hamiltonian of one
hole in the $t-J$ model on a triangular lattice in spin wave approximation.
In the following, we analyze its content by treating the hole magnon coupling in the simplest approximation.

\subsection{Born approximation of the selfenergy}
\begin{figure}[hbt]
\setlength{\epsfxsize}{\columnwidth}
\centerline{\epsfbox{fig1.eps}}
\caption[Spectra]{Spectral density $A({\bf k},\omega)$ in SCBA approximation
for $N_s=36 \times 36$ sites, $t=J=1$, and for $\bf k$ values taken along
a straight line from $\Gamma$ to K (cf. Fig. \ref{BZ}) ($\eta=0.1$).}
\label{kspectra}
\end{figure}
Following previous treatments of the square lattice case \cite{Marsiglio91},
we employ the SCBA to obtain the selfenergy $\Sigma({\bf k},\omega)$
of one hole.
We denote the Green's function of one hole by
$G({\bf k},\omega)=(\omega-\epsilon_{\bf k}-\Sigma({\bf k},\omega))^{-1}$.
Then,
\begin{eqnarray}
\Sigma^{SCBA}({\bf k},\omega)\!\!
&=&\frac{1}{N_s}\sum_{\bf k'}
{\left|u_{{\bf k}-{\bf k'}}f_{{\bf k},{\bf k'}} +v_{\bf k-k'}f^{*}_{{\bf k'},{\bf k}}\right|}^2 \times \nonumber\\
&&G^{SCBA}({\bf k'}, \omega- \omega_{\bf k-k'}) \; .
\label{Sigma}
\end{eqnarray}
Here, $\omega_{\bf q}=\frac{3J}{2}\sqrt{(1+2w_{\bf q})(1-w_{\bf q})}$ is the
spin wave energy.
$u_{\bf q}$ and $v_{\bf q}$ are the Bogoliubov amplitudes,
\begin{eqnarray}
u_{\bf q}&=&{\left\{\frac{1}{2}\left[\frac{3J(1+w_{\bf q}/2)}{2\omega_{\bf q}}+1\right]\right\}}^{1/2} \nonumber\\
v_{\bf q}&=&\mbox{sgn}( w_{\bf q}){\left\{\frac{1}{2}\left[\frac{3J(1+w_{\bf q}/2)}{2\omega_{\bf q}}-1\right]\right\}}^{1/2}.\nonumber
\end{eqnarray}
From the Green's function, the spectral density is obtained as
$A({\bf k},\omega)=-\frac{1}{\pi} \lim_{\eta \to 0^+}
\mbox{Im}\,G({\bf k}, \omega+i\eta)$.
The parameter $\eta$ regularizes the spectral density.
\end{multicols}
\widetext
\renewcommand{\thefootnote}{\fnsymbol{footnote}}
\begin{table}[bt]
\begin{tabular}{||c||c|c||c||c|||c|c||c||cc||}
&\multicolumn{4}{c|||}{exact diagonalization}&\multicolumn{4}{c}{linear spin wave, SCBA}& \\ \hline
&\multicolumn{2}{c||}{$t=0$}&$t=0.1$&$t=1$&\multicolumn{2}{c||}{$t=0$}&$t=0.1$&$t=1$&\\ \hline
&$n_h=0$&$n_h=1$&$n_h=1$&$n_h=1$&$n_h=0$&$n_h=1$&$n_h=1$&$n_h=1$&\\
$N_s$&$E^{ex}_{0}$&$E^{ex}_{1,loc}$&$\delta E^{ex}_{1}$&$\delta E^{ex}_1$&$E^{LSW}_{0}$&$E^{SCBA}_{1,loc}$&$\delta E^{SCBA}_1$&$\delta E^{SCBA}_1$&\\ \hline\hline
9 & -5.25000&0.50000&0.40000&4.00000& -5.62500&0.66884&0.31627&3.18974&\\
12& -7.32396&1.15197&0.38544&4.09035& -7.25658&0.64520&0.32854&3.39377&\\
21&-11.78091&0.56862&0.39986&4.06326&-11.82919&0.65145&0.32504&3.35476&\\
24\footnotemark[2]&-12.93870&0.92897&0.29581&3.42937&-13.04174&0.65227&0.32561&3.36573&\\
27&-15.12597&0.59201&0.38805&3.99864&-15.04634&0.65052&0.32572&3.36510&\\
\end{tabular}
\caption{Exact and approximate groundstate energies of samples of $N_s$ sites
of the $t-J$ model with $n_h(=0,1)$ holes. $E_0$: groundstate energies in the half filled case. $E_{1,loc}$: energies for creating a localized hole.
$\delta E_1$: energy gain of the hole due to delocalization.}
\label{groundstate}
\end{table}
\begin{multicols}{2}
\narrowtext
\footnotetext[2]{For $N_s=24$ the crystal momentum of the one hole groundstate is
an interior point close to K of the Brillouin zone. This is the reason,
why for $N_s=24$ the values of $\delta E^{ex}_1$ deviate significantly from
the rest.}
\renewcommand{\thefootnote}{\arabic{footnote}}
(\ref{Sigma}) has been solved by numerical iteration starting with $\Sigma =0$
for a lattice of $N_s=36 \times 36$ sites with periodic boundary conditions.
In Fig.~\ref{kspectra} we display for $t=1$, $J=1$ the spectral density
$A({\bf k},\omega)$ on $\bf k$--points along a straight line from the centre
$\Gamma$ to the corner K of the Brillouin zone (cf.~Fig.~\ref{BZ}).
The main feature of the spectra is a pronounced quasiparticle peak.
For $t=0$, the quasiparticle dispersion is flat throughout the Brillouin zone.
For increasing $t$, a dispersion with the minimum at $\Gamma$ emerges and the
peak broadens.
Around $\Gamma$, the quasiparticle peak persists for values of $t$ up to $10J$;
near $K$ it already decays for $t>0.2J$.

\subsection{Comparison with exact numerical diagonalization results}
As we have pointed out in the course of the derivation, the effective
Hamiltonian ${\cal H}_{\Delta}$ is an approximate result, and the computation
of the one-hole Green's function is based on the self-consistent Born
approximation. In order to have a check on the validity of these
approximations, we computed the spectral density $A({\bf k},\omega)$ and
related quantities directly
for the $t-J$ model on small periodic samples of the triangular lattice
with $N_s$ sites. Numerically exact results for the quantities in question
were obtained by applying the Lanczos technique (see e.g. \cite{Dagotto94})
to the Hamiltonian of these samples.
In these computations, the exchange constant $J$ has been set equal to unity
throughout. Results for the groundstate energies for half filling ($n_h=0$) and
for one hole ($n_h=1$) are displayed in Table \ref{groundstate} together with
the approximate LSW and SCBA energies for the same sample sizes.
For $t\neq 0$, the groundstate wave function of the hole is an extended state
with crystal momentum at the high symmetry points of the Brillouin zone;
$\Gamma$ for odd $N_s$ and K for even $N_s$.

\begin{figure}[t]
\begin{minipage}[t]{0.95\columnwidth}
\setlength{\epsfxsize}{\columnwidth}
\centerline{\epsfbox{fig2.eps}}
\caption[Brillouinzone]{The Brillouin zone of the $N_s=21$ system shows
a sixfold symmetry.}
\label{BZ}
\end{minipage}
\end{figure}
For the half filled case, the $t-J$ Hamiltonian reduces to the Heisenberg
Hamiltonian, and it is well known that in this case the LSW results $E^{LSW}_0$
are in good agreement with the exact results $E^{ex}_0$, in particular for the
larger system sizes \cite{Bernu94}. Turning to the one-hole results, we first
discuss the case $t=0$ in which the hole is localized. $E_{1,loc}$ is the
energy needed to create a localized hole in the half filled groundstate.
There is a strong even-odd staggering in the exact results (2nd column of Table
\ref{groundstate}): in the even samples ($N_s$ even) in which the spins pair
up to a singlet, $S_{tot}=0$, the 'binding energy' per electron is larger
than in the odd systems which contain an unsaturated spin, $S_{tot}=1/2$.
This is a finite size effect which, as is seen in Table \ref{groundstate},
decreases very slowly with the sample size. Nevertheless, the exact values
$E^{ex}_{1,loc}$ appear to converge to the SCBA value $E^{SCBA}_{1,loc}$ in an
alternating fashion. That the even-odd staggering is absent from
$E^{SCBA}_{1,loc}$ is understandable, since the SCBA is based on the spin wave
spectrum of the infinite sample.

\end{multicols}
\widetext
\begin{figure}
\begin{minipage}[b]{0.95\columnwidth}
\epsfxsize=0.49\columnwidth
\begin{minipage}[t]{\epsfxsize}
a)\\
\centerline{\epsfbox{fig3a.eps}}
\end{minipage}
\hfill
\epsfxsize=0.49\columnwidth
\begin{minipage}[t]{\epsfxsize}
b)\\
\centerline{\epsfbox{fig3b.eps}}
\end{minipage}
\caption[Exact and SCBA-Spectra]{Spectral density a) at the $\Gamma$ point
and b) at the corner K of the Brillouin zone for $t=0.1$ and $t=1$ for $J=1$.
The solid line shows the exact results for the $N_s=21$ sites, the dashed
(dotted) line the result of the SCBA for $N_s=21$ ($N_s=36 \times 36$) sites.
$\omega$ is measured against $E^{ex}_{0}$ and $E^{LSW}_{0}$ ($\eta=0.1$).
\label{spectra2}}
\end{minipage}
\end{figure}
\begin{multicols}{2}
\narrowtext
For finite hopping amplitude $t\neq 0$, the
hole becomes delocalized. It is suggestive to write the hole energy as
$E_1=E_{1,loc}-\delta E_1(t)$, where $\delta E_1(t)$ is the energy gain due to
delocalization of the hole wave function. The results in Table
\ref{groundstate} show that $\delta E_1$ increases linearly with $t$,
$\delta E_1(t) = \alpha t$. This assertion has been verified by computing
$\delta E_1(t)$ for a sequence of values $0.1 <t<1$ not shown in Table
\ref{groundstate}. The coefficient $\alpha$ is seen to differ significantly
between the exact results and the SCBA, $\alpha^{ex}\approx 4$,
$\alpha^{SCBA}\approx3.36$. At present, we are not in a position to decide whether
this discrepancy is inherent in the effective Hamiltonian
${\cal H}_{\triangle}$ or whether it is a deficiency of the SCBA.

Next we compare the exact and the SCBA results for the spectral density
$A({\bf k},\omega)$. Fig.~\ref{spectra2} shows the spectral density of one
hole in the $N_s=21$ sample at the centre ($\Gamma$) and at the corner (K) of
the Brillouin zone (cf. Fig.~\ref{BZ}) for the parameter values  $J=1$ and
$t\!=\!0.1$, $t=1$. The solid lines are the results of the exact diagonalization
which were  obtained from a continued fraction expansion \cite{Haydock72} of
the Lanczos results. The dashed lines are the result of the SCBA for $N_s=21$.
For $t\!=\!0.1$ there is a well defined quasiparticle peak in the exact results
at the bottom of the spectrum. This peak is nicely reproduced by the SCBA.

For $t\!=\!1$, a quasiparticle peak is still visible at $\Gamma$ while
one finds a broad structure at the corner of the Brillouin zone. The SCBA
reproduces the peak in the spectrum at $\Gamma$; however, its
position is shifted to higher energies. At K, the SCBA spectrum
shows a structure which becomes broader when the system size is increased from
$N_s\!=\!21$ to $N_s\!=\!36 \times 36$ (dotted lines).
On the other hand, in all cases where we find a quasiparticle peak, the SCBA
results for $N_s\!=\!21$ and for $N_s\!=\!36\times 36$ are indistinguishable.
Thus we conclude that for $t=1$ the quasiparticle peak disappears if one
changes the wavevector from the $\Gamma$ point to the corner of the Brillouin zone, cf. Fig.~\ref{kspectra}.
While there remain differences, we find that overall the SCBA reproduces the
qualitative features of the exact results.
\begin{figure}[tb]
\setlength{\epsfxsize}{\columnwidth}
\centerline{\epsfbox{fig4.eps}}
\caption[Dispersion]{The dispersion of one hole as defined in the text for $t=0.1$, $J=1$ and $N_s=21$
sites. The symbols $\circ$ show the exact results, the diamonds $\diamond$ the
results of the SCBA and the squares $\Box$ the lowest order approximation for
the Green's function.}
\label{dispersion}
\end{figure}

Finally we discuss the energy dispersion of one hole. We define the dispersion
as the difference of the position of the maximum of $A({\bf k},\omega)$
for a given ${\bf k}$ and the one hole creation energy $E^{SCBA}_{1,loc}$ (see
Table \ref{groundstate}), i.e. the position of the
maximum for $t=0$. In Fig.~\ref{dispersion}, we show the dispersion for
$N_s\!\!=\!\!21$ sites for $t=0.1$ and $J=1$. The circles (connected by solid
lines) show the results of the exact diagonalization. They follow closely the
free dispersion of the hole, $\epsilon_{\bf q}-3J/4=-3\,t\,w_{\bf q}$
(shown as boxes). The SCBA (diamonds) yields an improvement towards the
exact results for all points of the Brillouin zone. Obviously, the free
dispersion is already a good approximation of the exact results.

\section{Summary}
In this work, we have developed a formalism which allows the derivation of
effective Hamiltonians for the motion of holes in an arbitrarily ordered spin
background. Fundamental to this development was the construction of a coherent
state approximation for the electron states, which automatically excludes double
occupancy. In this representation, the partition function of an arbitrary number
of holes can be cast into the form of a path integral which still contains the
full non-linear coupling of the holes to the spin degrees of freedom of the
background. As a first application of this formalism, we have rederived the
well known effective Hamiltonian ${\cal H}_{\Box}$ for the motion of a single
hole in the collinear antiferromagnetic order of the square lattice
antiferromagnet in the linear spin wave approximation. The derivation of the
effective
\begin{figure}[bt]
\setlength{\epsfxsize}{\columnwidth}
a)\hspace{4.5cm}b)\\
\centerline{\epsfbox{fig5.eps}}
\caption{Spin arrangement of $|\Phi_{\bf r}\!>$ (top) and $c^{}_{{\bf r} + \mbox{\boldmath
$\scriptstyle \delta$} \uparrow} c^{\dagger}_{\bf r \uparrow} |\Phi_{\bf r}\!>$ (bottom) for a) the square lattice AF and b) the triangular AF.
\label{config}}
\end{figure}
Hamiltonian
${\cal H}_{\triangle}$ of a single hole moving in the planar spin arrangement
of the triangular antiferromagnet also makes use of the linear spin wave
approximation. However, in this case, special care has to be taken to ensure a
proper treatment of the Goldstone modes which must not couple to the hole.
In contrast to the square lattice AF, where hopping of the hole from a lattice
site ${\bf r}$ to a neighbouring site {\boldmath $r \unboldmath{+}\delta$} is necessarily
accompanied by a {\em spin flip} at site $\bf r$, the same hopping process
requires only a {\em rotation of the spin} at ${\bf r}$ by
$\pm{120}^{\small o}$ in the case of the triangular AF, see Fig \ref{config}.

In other
words, if $|\Phi^{(0)}_{\bf r}\!>$
is the groundstate with one hole at ${\bf r}$ in
the undistorted spin background of the AFs, then the hopping matrix element
$<\!\Phi^{(0)}_{{\bf r} +\mbox{\boldmath $\scriptstyle \delta$}}\!|c_{{\bf r}+\mbox{\boldmath $\scriptstyle \delta$} \sigma}c^{\dagger}_{{\bf r}\sigma}|\Phi^{(0)}_{\bf r}\!>$ is always zero for the square lattice AF, while it is $+\frac{1}{2}$ for
the triangular AF. This accounts for the main difference between the hole
dynamics in the collinear square lattice AF and the planar triangular AF.

On the square lattice, the hole can hop due to the zero point fluctuations of
the AF background. In this case, magnon-assisted hopping happens
predominantly between the sites of the same magnetic sublattice. This leads to
a minimum of the hole dispersion at a quarter of a reciprocal lattice vector
of the square lattice. By contrast, on the triangular lattice, hole hopping
between nearest neighbour sites, i.e. between different magnetic sublattices,
is also possible without magnon assistance. Thus, for $J>>t$, where magnon
assisted processes are energetically suppressed, the hole dispersion in the
triangular AF will be dominated by the bare (unassisted) hopping processes.
This has been confirmed by comparing the exact dispersion of the bare hole in
the 21 site sample for $t=0.1 J$. The approximate inclusion of the
magnon-assisted processes in the calculation of the dispersion by the
self-consistent Born approximation has been found to improve the agreement
with the exact dispersion.
The exact one--hole Lagrangian (\ref{Lkin}-\ref{Lj}), evaluated in spin wave
approximation, leads to results in reasonable agreement with exact numerical
diagonalization of small systems. ${\cal L}$ provides thus a firm basis for a
derivation of a continuum model which is capable of describing the full
non--linearities of the spin fields in the presence of single holes.
\end{multicols}
\widetext

\begin{appendix}
\begin{multicols}{2}
\narrowtext
\section{}
A straightforward expansion of $\cal L$ around the classically ordered state
with respect to the fields $\theta$ and $\phi$, and a subsequent integration
of $\psi$ leads to the appearance of zero energy spin wave amplitudes
in linear order in the hopping term ${\cal L}_t$.
This is in contradiction to the spin rotational invariance of the model
(\ref{t-J}).
In order to resolve the contradiction, we now verify that this invariance
persists in an appropriate spin wave expansion.
In the first order expansion around the state
given by $\phi^{}_{\bf r}=\phi^{(0)}_{\bf r}$, $\theta_{\bf r}=\frac{\pi}{2}$
(cf.~\ref{coorsq}), the critical term ${\cal L}_t$ reads
\begin{eqnarray}
{\cal L}_t = && -t \sum_{<\!{\bf r}, {\bf r'}\!>}
 \left\{ \eta^*_{\bf r'} \eta^{}_{\bf r^{}}
 e^{-\frac{i}{2}(\psi_{\bf r'}-\psi_{\bf r^{}})}
 \left[
\cos(\frac{\phi^{(0)}_{\bf r^{}}-\phi^{(0)}_{\bf r'}}{2})
 \right. \right.  \nonumber \\
&& \left. - \sin(\frac{\phi^{(0)}_{\bf r^{}}-\phi^{(0)}_{\bf r'}}{2})
 \left( i \frac{p_{\bf r}+p_{\bf r'}}{\sqrt{2}}
       + \frac{x_{\bf r}-x_{\bf r'}}{\sqrt{2}} \right) \right]\nonumber\\
&& \left. +  \;\;{\bf r} \leftrightarrow  {\bf r'}   \right\}            \; .
\label{Lt1st}
\end{eqnarray}
This expression is valid for both the square, and the triangular lattice.
We now perform an infinitesimal homogeneous rotation in spin space
parametrized by the angles {\boldmath $\epsilon$}.
The corresponding transformation of the fields can be read off from (\ref{coh}).
The field $\eta$ is unchanged and the linear changes in $\psi$, $\theta$, and
$\phi$ are (we express the last two fields by x and p)
\begin{eqnarray}
\psi_{\bf r}' &=&\psi_{\bf r}+2\left[ \epsilon^{x} \cos \phi^{(0)}_{\bf r} +
\epsilon^{y} \sin \phi^{(0)}_{\bf r}\right]\nonumber\\
x_{\bf r}' &=&x_{\bf r} +\sqrt{2}\epsilon^{z}\nonumber\\
p_{\bf r}' &=&p_{\bf r} +\sqrt{2}\left[-\epsilon^{x} \sin\phi^{(0)}_{\bf r}+
\epsilon^{y} \cos\phi^{(0)}_{\bf r}\right].
\label{inftf}
\end{eqnarray}
Substituting these rotated fields for the original ones in (\ref{Lt1st}),
one sees that $\epsilon^{z}$
drops out and the change
in the field $p_{\bf r}$ induced by the other two rotations
$\epsilon^{x}$ and $\epsilon^{y}$ is compensated
by the corresponding change in the field $\psi_{\bf r}$.
Thus, we see that ${\cal L}_t$, and hence the whole Lagrangian, is invariant
under an infinitesimal rotation in spin space as it should be.
It is only after the integration over the field $\psi$ that the invariance
appears to be lost.

Turning to the case of the square lattice, where
$\phi^{(0)}_{\bf r} = \pm \pi / 2$ ($\cos\phi^{(0)}_{\bf r} =0$),
the zero modes are seen to decouple in $\psi_{\bf r}$ and $p_{\bf r}$ (cf. (\ref{inftf})), and in ${\cal L}_t$
the term of zeroth order in the fields $x_{\bf r}$ and $p_{\bf r}$ vanishes.
It is easily verified from the spin wave expansion of ${\cal L}_J$
that the zero modes are given by
$x_{\bf r} = x$, $p_{\bf r} = 0$ and
$x_{\bf r} = 0$, $p_{\bf r} = p \sin\phi^{(0)}_{\bf r}$
which both cancel in ${\cal L}_t$.
After substituting $\eta \,e^{\frac{i}{2}(\psi - \phi^{(0)})}$ by $h$,
we can integrate over $\psi$, and return to the operator form.
Thus, the spin wave expansion as sketched in the main text leads to
the correct result \cite{Marsiglio91}.

In the case of the triangular lattice, where
$\phi^{(0)}_{\bf r}=\frac{2\pi}{3},0,-\frac{2\pi}{3}$ for the three
sublattices respectively, the zero modes in $\psi_{\bf r}$ and $p_{\bf r}$ mix.
Again, it is easily verified from the spin wave expansion of ${\cal L}_J$
that they are given by $x_{\bf r} = x$, $p_{\bf r} = 0$, and
$x_{\bf r} = 0$, $p_{\bf r} = p \sin\phi^{(0)}_{\bf r}$, and $x_{\bf r} = 0$, $p_{\bf r} = p \cos\phi^{(0)}_{\bf r}$.
The first mode cancels in ${\cal L}_t$, but the last two remain, if one
disregards $\psi$.
However, we are free to apply a canonical transformation to the fields $\psi$,
$x$, and $p$ in the path integral. We choose
\begin{eqnarray}
\psi_{\bf r}&\to& \psi_{\bf r}+\sqrt{\frac{2}{3}}\left(p_{\bf r}+\frac{2}{3}
\sum_{j=1}^3p_{{\bf r}+{\mbox{\boldmath $\scriptstyle \delta$}_j}}\right)\nonumber\\
x_{\bf r}& \to & x_{\bf r} +\sqrt{\frac{1}{6}}\left(\eta^{*}_{\bf r}\eta^{}_{\bf r} + \frac{2}{3}\sum_{j=1}^{3} \eta^{*}_{{\bf r}-{\mbox{\boldmath $\scriptstyle \delta$}_j}}\eta^{}_{{\bf r}-{\mbox{\boldmath $\scriptstyle \delta$}_j}}\right)\nonumber\\
p_{\bf r}&\to&p_{\bf r}
\label{A3}
\end{eqnarray}
($\mbox{\boldmath $\delta$}_j = (\cos \varphi_j, \sin \varphi_j)$,
$\varphi_j = \frac{2\pi}{3}j$ are the three nearest neighbour vectors.)
With this choice ({\it i}) the new field $\psi$
remains invariant under homogeneous rotations in spin space, i.e. it does not
contain a zero mode, and ({\it ii}) ${\cal L}_{kin}$ is changed only by a
total time derivative which yields no change in the action
(the latter condition is equivalent to the transformation being canonical).
After applying (\ref{A3}) to ${\cal L}$, all zero modes cancel in ${\cal L}_t$.
We substitute $\eta \,e^{\frac{i}{2}(\psi - \phi^{(0)})}$ by $h$,
integrate over $\psi$, and return to the operator representation.
The result for ${\cal H}_{\triangle}$ is the expression (\ref{H3}).

\end{multicols}
\widetext
\end{appendix}

\begin{multicols}{2}
\narrowtext

redpajama_set_name: RedPajamaArXiv


The fanfare kicking off Clear Space Theatre's production of "The Music Man" may not include 76 trombones, but the show itself will feature that very tune! Meredith Willson's Tony Award-winning show - it won five, including the award for Best Musical - runs through Sunday, March 31.
So strike up the band and join "Professor" Harold Hill (Drew Colegrove) as he works an elaborate con, aimed at relieving the residents of River City, Iowa of their cash - under the guise of saving their youth from demon pool. ("…Ya got trouble, folks. Right here in River City! Trouble with a capital "T" and that rhymes with "P" and that stands for pool!") And delight in the unexpected course his efforts take as he becomes enamored of Marian, the local librarian and part-time music teacher (Marian Sunnergren).
Sponsored by WMDT TV47, "The Music Man" runs weekends through Sunday, March 31. Friday and Saturday performances are at 7 p.m., and Sunday performances are at 3 p.m. Tickets for all shows are $17 to $32, and may be purchased on-line at www.clearspacetheatre.org, or by calling the box office at 302-227-2270.


text:
India, Malaysia to fight Islamic State together: Najib Razak
April 3, 2017 Abha ManakatalaLeave a Comment on India, Malaysia to fight Islamic State together: Najib Razak
Narendra Modi hails mutual recognition of academic degrees
India and Malaysia on Saturday agreed to cooperate to defeat Islamic State militants and the growing threat of radicalisation and extremism. Visiting Malaysian Prime Minister Najib Razak held talks here with Prime Minister Narendra Modi and sealed six agreements, while extending support to India for a greater role in the maritime security of the Asia-Pacific region.
"Malaysia and India will cooperate to fight the IS [Islamic State] and deal with radicalisation. We will also share our experience of de-radicalisation with India. We plan to hold a major conference on de-radicalisation jointly," Prime Minister Razak said during his statement to the media at Hyderabad House, explaining that India and Malaysia ties are at a "historic high".
Greater synergy
Mr. Razak, who spent a day in Chennai upon his arrival in the country on Thursday, expressed support for greater synergy with India on the security front, especially in the maritime domain, and said, "We appreciate the greater role of India in the maritime security of the Asia-Pacific region." The visiting delegation's comments on the maritime issue is significant as both the countries have been demanding freedom of navigation in the South East Asian region, where China has been flexing muscles and has claimed most of the South China Sea.
The visiting dignitary's comments about greater cooperation to fight the extremism of the IS followed the exchange of six bilateral agreements.
Both sides signed agreements on air services, sports, human resources, palm oil production and research, and technological development. An agreement that will allow India to build a fertilizer plant in Malaysia was also signed.
In his statement, Mr. Modi described the fertilizer plant as an important development. He urged Malaysia to participate in India's infrastructure sector and said that bilateral defence has come to cover training and maintenance in the military field. Mr. Modi also highlighted educational cooperation and said, "Mutual recognition in educational degrees is a landmark development".
A bilateral joint statement issued by the India-Malaysia CEOs Forum emphasised the need for visa-free travel for Indians and Malaysians as travel and tourism in both countries contribute to their economic growth. "Additionally, Malaysia should support and champion the introduction of the ASEAN common visa for travellers from outside the region, including India," the statement said.
Both sides also highlighted that Malaysia would allow Indian Ayurveda and Siddha practitioners to serve in that country. As part of the move to popularise courses in Ayurveda, the government of Malaysia and the Universiti Tunku Abdul Rahman would provide courses in Ayurveda.
Highway liquor ban to hit 40% outlets, say analysts
Now, China flags Tawang rail link
Damocles sword hangs over Jharkhand's senior IAS officer
February 10, 2013 JharkhandNews
PLFI ultras blow up Mobile Tower in Simdega
December 27, 2014 Abha Manakatala
Hemant Soren to hand over appointment letters to 124 Dy.Magistrates
August 4, 2013 August 4, 2013 JharkhandNews


"Dialog Method" is a newly coined word by the present writer. That is based on only "active listening", one of the basic skills used for counseling, as "paraphrase" and "clarification".
This method has a rule that "Before telling our own opinion or feeling, we must confirm what the other party wants to tell". This rule must be put into practice in our daily life as the occasion demands. "Confirmation", a response using words, decreases misunderstanding and increases a relationship of mutual trust.
The primary purpose of "Dialog Method" is a making of better human relations in our daily life. But instructing a client in "Dialog Method" is useful for improving in skills of personal relationships and after care of counseling. Instructing is carried out not only during interview but also in the activities named "Dialog Group" which aims at practicing "Dialog Method".
The group presents mental safety to all members and is useful for getting rid of stress and prevention of anguish of heart in our daily life.


Is foundation of building a tension member or compression member, explain the conditions?
Which type of construction don't specified in Google maps?
What type of foundation will be adopted in the clayey soil present in Kuttanadu?


text:
La gastronomía coahuilense son los alimentos, técnica culinarias y platos típicos del estado de Coahuila, en Aridoamérica y en el Noreste de México.

Como en todo el país, los ingredientes esenciales de su dieta son el maíz, el chile y el frijol. Coahuila también es famoso por sus carnes frescas: cabrito, carnero y ternera. Algunos platos típicos de Coahuila son el asado de puerco, la fritada norteña, la machaca, el cabrito salteado o al pastor, los burritos o los tamales «de dedo». En Coahuila, concretamente en Piedras Negras, nacieron los famosos nachos. En cuanto a chiles, se utilizan mucho el guajillo, el pasilla y cascabel.

Coahuila también tiene mucha tradición vinícola, produciendo vino, brandy y otros aguardientes ya desde el siglo XVI.

Productos
Coahuila es un estado desértico, por lo que la superficie apta para la agricultura se reduce al 4.97% (~753.000 ha) de su territorio. Sin embargo el área agrícola coahuilense consta de ~300.000 ha, de las cuales casi la mitad son cultivos de temporal (44%) y lo demás, cultivos de riego (56%).

Tortillas de harina de trigo, típicas de todo el norte de México.
Carnes: la gastronomía coahuilense es ideal para los paladares más carnívoros.
 El sector bovino es el más numeroso, y se encuentran razas Charolais, Beefmaster, Hereford, Brahamn y Braford. Un producto apreciado es el becerro, la cría lactante de la vaca.
La leche de vaca, pues Coahuila produce un 11.6% del total nacional, gracias a la explotación intensiva.
Queso asadero, un tipo de queso fresco elástico como el queso Oaxaca.
Quesos de frutas y frutos, como de higo, de piñón, de uva o de nuez, artesanales de Arteaga.
El sector caprino, también tiene especial importancia. Algunas razas son la cabra alpina, la Nubia, Saanen y Criolla. Un producto estrella coahuilense es el cabrito, cría lactante de cabra
La leche de cabra, cuya producción coahuilense representa un 35.7% del total nacional.
 Otras carnes también con mucha presencia son la avícola (guajolote, codorniz, pato...) y la porcina.
Producción frutal del Sureste, entre las que destacan las manzanas de Arteaga, los higos, duraznos, ciruelas, chabacanos, uvas y melones.
Sorgo forrajero
Nuez
Quesos de frutas y frutos de Arteaga

Todos los datos mostrados en esta sección están recogidos en el Programa Estatal de Desarrollo Rural 2011–2017 del Gobierno de Coahuila. Coahuila fue un importante productor de trigo, aunque su siembra prácticamente ha desaparecido hoy día.

Antojitos y platillos

 Discada o chatarra, mezcla de carnes asadas en un disco para arar, de ahí su nombre. Tradicionalmente incluye chorizo, tocino, filete de cerdo y aguayón de res, a veces carne molida, jamón y salchicha, condimentados con chile poblano o jalapeño, cebolla, jitomate y a veces, pimientos y/o cilantro. Se sirve con tortillas y frijoles, y suele ser motivo de reunión con los seres queridos.
 Enchiladas estilo coahuilense o norteño, rellenas de queso asadero y rajas también llamadas enchiladas de olla, porque se cuecen en una olla, y la salsa roja elaborada con cebolla, ajo y chile ancho.
Gorditas, tienen gran tradición en el estado, tanto las de harina de maíz como las de trigo. En Matamoros y otras áreas de La Laguna es común encontrar gorditas de cocedor, también llamadas de horno, rellenas de chicharrón, frijoles, queso...
Tamal: al igual que en toda la República, en Coahuila se consumen ampliamente los tamales, sin embargo, suelen ser de menor tamaño. Este pequeño formato es conocido como «tamal de dedo». En cambio, tienen más relleno que masa.
Norteños, rellenos de carne deshebrada, machaca o queso asadero, con un adobo de chiles rojos.
De dulce, por ejemplo, de pera, membrillo y canela.

Postres y dulces

Leche quemada, típico de Viesca y de toda la Comarca Lagunera, se suele confundir con el jamoncillo por el uso de nuez, o también con la cajeta, una especie de dulce de leche. Básicamente consiste en hervir leche (mezclada de chiva y de vaca) con azúcar blanco y canela por 3-5 h. Una vez seco se decora con nuez y coco.
Pan de pulque, un tipo de pan dulce o salado que incluye pulque en su masa, proporcionándole su característico sabor intenso. Al parecer, tiene su origen en Tlaxcala, cuando en la época colonial se introdujo el pan, pero importar levadura desde el Viejo Mundo era muy costoso y se debía fermentar la masa con pulque tlachique. Más tarde el pan de pulque se extendería por otros estados del centro de México y al sureste de Coahuila. También se lo conoce como «pan de burro» puesto que el pulque se trasladaba sobre dicho animal.
Semita chorreada, un plato nacido en el vecino estado de Nuevo León, una cemita dulce con piloncillo.

Bebidas

Vino
Los viñedos coahuilenses son de los más antiguos de América; en 1594, un grupo de jesuitas estableció la misión de Santa María de las Parras trayendo las primeras uvas en suelo americano y produciendo los primeros vinos. La primera bodega en establecerse fue la todavía existente Casa Madero, cuya licencia fue otorgada por el rey español Felipe II en 1597. En julio de 2019 el Ayuntamiento de Saltillo presentó la Ruta Vinos y Dinos, una ruta turística que combina casas vinícolas y áreas de interés paleontológico. que comienza en Parras de la Fuente, ciudad vitivinícola por excelencia, y sigue, entre otros, por Cuatro Ciénagas y Arteaga, ambos pueblos mágicos. Se produce vino y brandy.

Pulque
El pulque es una bebida alcohólica fermentada mexicana producida con aguamiel mezclada con frutas y verduras para darles un nuevo sabor. El pulque tiene, además, varios beneficios asociados: trata el insomnio por su contenido de melatonina. También contiene lactobacilos que ayudan a la digestión y problemas gastrointestinales como la gastritis. También combate la anemia.

Ferias gastronómicas
Algunas ferias gastronómicas en Coahuila son:

 Feria de la Manzana, en Arteaga (del 12 al 15 de septiembre)
 Fiesta de la Vendimia, en Parras de la Fuente (del 3 al 20 de agosto)

Referencias

Lectura complementaria

Véase también

 Anexo:Gastronomías regionales de México
 Gastronomía de México

Gastronomía de Coahuila

redpajama_set_name: RedPajamaWikipedia


JEDDAH: The tourism contact center of the Saudi Commission for Tourism and National Heritage (SCTH) addressed 14,633 complaints filed in 2018 through the center's 24-hour unified number 19988, which receives all complaints and suggestions from end users.
The complaints were related to services provided in tourist establishments, and mainly focused on accommodation services, travel agencies and tour operators across the Kingdom.
They also indicated administrative, systemic and pricing violations in various sectors that operate under the SCTH. Callers made 265 suggestions for developing tourism services.
The contact center received 33,262 inquiries about tourism services in the Kingdom and provided information about nearly 2,400 offers and discounts during holidays. There were more than 33,000 inquiries about events held in Saudi Arabia.
Online platforms, smartphone apps and SCTH social media accounts have all contributed to reducing the volume of phone calls received by the tourism contact center.
SAHUC road show shed light to prospective Hujjaaj.


Text Photos from two Wagner albums, one standing upright and the other like a book, both padded, in bad shape, originally red velvet, purchased at an antique fair near State College, Pennsylvania. Contact pizzo2@embarqmail.com for more information.
This picture was identified as "Aunt Hattie, Grandpa Wagner, Aunt Amy"
labelled "Uncle Ephraim Wagner -- Grandpa's brother -- lived in Shartlesville"
Unlabelled, but think these are correct family members.
Back of photo has notation "Give one to Kate's parents"
Wagner Album, #52 Luetta Wagner ?
on back: "Change of Locality, Photographed by Chas. A. Saylor, at the New Gallery, over Heizmann's, one square below the Rail Road. No work allowed to leave this Establishment that is not perfectly satisfactory"
E. J. Zerbe, Photographer, Rehrersburg, Berks Co. Pa.
W. S. Anspach, Lebanon, Pa.
Wm. B. White, Photographer, Freeport, Ill.
Chas. A. Saylon Photograph Gallery in Reading, Pa.
Inscribed on back "To Mother"
Patton & Dietrich's Photograph Gallery, Reading, Pa.
W. McHenry, Photographer, Freeport, Ill.
W. S. Anspach, Photographer, Lebanon, Pa.