image
imagewidth (px) 3
1.29k
| latex
stringlengths 3
4.96k
| latex_norm
stringlengths 5
5.62k
| page_id
stringlengths 15
15
| expr_type
stringclasses 2
values |
|---|---|---|---|---|
$S(\phi )$ | $ S ( \phi ) $ | 0001015_page002 | embedded |
|
$\phi $ | $ \phi $ | 0001015_page002 | embedded |
|
$\exp (-Ht)$ | $ e x p ( - H t ) $ | 0001015_page002 | embedded |
|
$\psi (x)$ | $ \psi ( x ) $ | 0001015_page002 | embedded |
|
$d\mu $ | $ d \mu $ | 0001015_page002 | embedded |
|
$x$ | $ x $ | 0001015_page002 | embedded |
|
$x(t)$ | $ x ( t ) $ | 0001015_page002 | embedded |
|
$V$ | $ V $ | 0001015_page002 | embedded |
|
$H= L +V(x)$ | $ H = L + V ( x ) $ | 0001015_page002 | embedded |
|
$L$ | $ L $ | 0001015_page002 | embedded |
|
$x(t)$ | $ x ( t ) $ | 0001015_page002 | embedded |
|
\begin {equation} H = \half p^2 + V(x) \end {equation} | \begin{equation*} H = \frac { 1 } { 2 } p ^ { 2 } + V ( x ) \end{equation*} | 0001015_page002 | isolated |
|
\begin {equation}\label {EVeq} \exp (-Ht) \psi (x) = \int d\mu \exp \left ( -\int _0^t V((x(s)) ds \right ) \psi (x(t)) \end {equation} | \begin{equation*} \operatorname { e x p } ( - H t ) \psi ( x ) = \int d \mu \operatorname { e x p } ( - \int _ { 0 } ^ { t } V ( ( x ( s ) ) d s ) \psi ( x ( t ) ) \end{equation*} | 0001015_page002 | isolated |
|
$x: I \to M$ | $ x : I \rightarrow M $ | 0001015_page003 | embedded |
|
$I$ | $ I $ | 0001015_page003 | embedded |
|
$[0,t]$ | $ [ 0 , t ] $ | 0001015_page003 | embedded |
|
$M$ | $ M $ | 0001015_page003 | embedded |
|
$n$ | $ n $ | 0001015_page003 | embedded |
|
$g$ | $ g $ | 0001015_page003 | embedded |
|
$\omega =dh$ | $ \omega = d h $ | 0001015_page003 | embedded |
|
$M$ | $ M $ | 0001015_page003 | embedded |
|
$\omega = \Omu (x) d\Xmu $ | $ \omega = \omega _ { \mu } ( x ) d x ^ { \mu } $ | 0001015_page003 | embedded |
|
$\omega = \Omu (x) d\Xmu $ | $ \omega = \omega _ { \mu } ( x ) d x ^ { \mu } $ | 0001015_page003 | embedded |
|
$\dot {x}^{\mu }(t')= \frac {d{x}^{\mu }}{d t'}$ | $ \dot { x } ^ { \mu } ( t ^ { \prime } ) = \frac { d x ^ { \mu } } { d t ^ { \prime } } $ | 0001015_page003 | embedded |
|
$S[x(.)] = i(h(x(t))-h(x(0)))$ | $ S [ x ( . ) ] = i ( h ( x ( t ) ) - h ( x ( 0 ) ) ) $ | 0001015_page003 | embedded |
|
$x(t)$ | $ x ( t ) $ | 0001015_page003 | embedded |
|
$\omega =0$ | $ \omega = 0 $ | 0001015_page003 | embedded |
|
$h$ | $ h $ | 0001015_page003 | embedded |
|
$M$ | $ M $ | 0001015_page003 | embedded |
|
$\omega =dh$ | $ \omega = d h $ | 0001015_page003 | embedded |
|
$\Pmu $ | $ p _ { \mu } $ | 0001015_page003 | embedded |
|
$\Xmu $ | $ x ^ { \mu } $ | 0001015_page003 | embedded |
|
$n$ | $ n $ | 0001015_page003 | embedded |
|
$H(p,x)= \Pmu \Xmu - \Lag (x,\dot {x})$ | $ H ( p , x ) = p _ { \mu } x ^ { \mu } - L ( x , \dot { x } ) $ | 0001015_page003 | embedded |
|
$H(p,x)= \Pmu \Xmu - \Lag (x,\dot {x})$ | $ H ( p , x ) = p _ { \mu } x ^ { \mu } - L ( x , \dot { x } ) $ | 0001015_page003 | embedded |
|
$\omega $ | $ \omega $ | 0001015_page003 | embedded |
|
$\Pb {\Tmu }{T_{\nu }}=0$ | $ \{ T _ { \mu } , T _ { \nu } \} = 0 $ | 0001015_page003 | embedded |
|
$\Pb {\Tmu }{H_c}=0$ | $ \{ T _ { \mu } , H _ { c } \} = 0 $ | 0001015_page003 | embedded |
|
$\Tmu $ | $ T _ { \mu } $ | 0001015_page003 | embedded |
|
$\psi (x)$ | $ \psi ( x ) $ | 0001015_page003 | embedded |
|
$\Pmu =-i \Dmu $ | $ p _ { \mu } = - i \partial _ { \mu } $ | 0001015_page003 | embedded |
|
$\Pmu $ | $ p _ { \mu } $ | 0001015_page003 | embedded |
|
$-i\DDmu $ | $ - i \nabla _ { \mu } $ | 0001015_page003 | embedded |
|
$\XXmu \psi =0$ | $ X ^ { \mu } \psi = 0 $ | 0001015_page003 | embedded |
|
$\XXmu =g^{\mu \nu } (p_{\nu } + i\omega _{\nu })$ | $ X ^ { \mu } = g ^ { \mu \nu } ( p _ { \nu } + i \omega _ { \nu } ) $ | 0001015_page003 | embedded |
|
\begin {equation}\label {ACeq} S[x(.)] = \Intot i\Omu (x(t'))\dot {x}^{\mu }(t') \, dt' \end {equation} | \begin{equation*} S [ x ( . ) ] = \int _ { 0 } ^ { t } i \omega _ { \mu } ( x ( t ^ { \prime } ) ) \dot { x } ^ { \mu } ( t ^ { \prime } ) \, d t ^ { \prime } \end{equation*} | 0001015_page003 | isolated |
|
\begin {equation}\label {MOMeq} \Pmu = \frac {\delta \Lag }{\delta \dot {x}^\mu } = i\Omu , \end {equation} | \begin{equation*} p _ { \mu } = \frac { \delta L } { \delta \dot { x } ^ { \mu } } = i \omega _ { \mu } , \end{equation*} | 0001015_page003 | isolated |
|
\begin {equation} \Tmu \equiv \Pmu - i\Omu . \end {equation} | \begin{equation*} T _ { \mu } \equiv p _ { \mu } - i \omega _ { \mu } . \end{equation*} | 0001015_page003 | isolated |
|
\begin {equation}\label {GTeq} \delta _{\epsilon }\psi (x) =-i \epsilon (\Dmu \psi (x) + \Omu (x) \psi (x)) \end {equation} | \begin{equation*} \delta _ { \epsilon } \psi ( x ) = - i \epsilon ( \partial _ { \mu } \psi ( x ) + \omega _ { \mu } ( x ) \psi ( x ) ) \end{equation*} | 0001015_page003 | isolated |
|
$\Etamu $ | $ \eta ^ { \mu } $ | 0001015_page004 | embedded |
|
$\Pimu $ | $ \pi _ { \mu } $ | 0001015_page004 | embedded |
|
$(2n,2n)$ | $ ( 2 n , 2 n ) $ | 0001015_page004 | embedded |
|
$\Etamu ,\Pimu $ | $ \eta ^ { \mu } , \pi _ { \mu } $ | 0001015_page004 | embedded |
|
$\nabla $ | $ \nabla $ | 0001015_page004 | embedded |
|
$\psi (x,\eta )$ | $ \psi ( x , \eta ) $ | 0001015_page004 | embedded |
|
$\Pmu =-i \DDmu $ | $ p _ { \mu } = - i \nabla _ { \mu } $ | 0001015_page004 | embedded |
|
$\Pimu = -i\frac {\partial }{\partial \Etamu }$ | $ \pi _ { \mu } = - i \frac { \partial } { \partial \eta ^ { \mu } } $ | 0001015_page004 | embedded |
|
$\psi (x,\eta )$ | $ \psi ( x , \eta ) $ | 0001015_page004 | embedded |
|
$(n,n)$ | $ ( n , n ) $ | 0001015_page004 | embedded |
|
$SM$ | $ S M $ | 0001015_page004 | embedded |
|
$\Xmu ,\Etamu $ | $ x ^ { \mu } , \eta ^ { \mu } $ | 0001015_page004 | embedded |
|
$Q$ | $ Q $ | 0001015_page004 | embedded |
|
$Q=\Etamu \Tmu =-i\Etamu (\Dmu + \omega )$ | $ Q = \eta ^ { \mu } T _ { \mu } = - i \eta ^ { \mu } ( \partial _ { \mu } + \omega ) $ | 0001015_page004 | embedded |
|
$Q=\Etamu \Tmu =-i\Etamu (\Dmu + \omega )$ | $ Q = \eta ^ { \mu } T _ { \mu } = - i \eta ^ { \mu } ( \partial _ { \mu } + \omega ) $ | 0001015_page004 | embedded |
|
$\chi $ | $ \chi $ | 0001015_page004 | embedded |
|
$\chi = \Pimu \XXmu = -ig^{\mu \nu } \Pimu (\nabla _{\nu }-\omega _{\nu })$ | $ \chi = \pi _ { \mu } X ^ { \mu } = - i g ^ { \mu \nu } \pi _ { \mu } ( \nabla _ { \nu } - \omega _ { \nu } ) $ | 0001015_page004 | embedded |
|
$M$ | $ M $ | 0001015_page004 | embedded |
|
$\psi (x,\eta )$ | $ \psi ( x , \eta ) $ | 0001015_page004 | embedded |
|
$Q=-i\Emh d \Eph $ | $ Q = - i e ^ { - h } d e ^ { h } $ | 0001015_page004 | embedded |
|
$\chi = \Eph \delta \Emh $ | $ \chi = e ^ { h } \delta e ^ { - h } $ | 0001015_page004 | embedded |
|
$d$ | $ d $ | 0001015_page004 | embedded |
|
$\delta = *d*$ | $ \delta = \ast d \ast $ | 0001015_page004 | embedded |
|
$h$ | $ h $ | 0001015_page004 | embedded |
|
$\chi =\Pimu \XXmu $ | $ \chi = \pi _ { \mu } X ^ { \mu } $ | 0001015_page004 | embedded |
|
$h$ | $ h $ | 0001015_page004 | embedded |
|
$Q$ | $ Q $ | 0001015_page004 | embedded |
|
$h$ | $ h $ | 0001015_page004 | embedded |
|
$H_g$ | $ H _ { g } $ | 0001015_page004 | embedded |
|
\begin {equation}\label {SPBeq} d\Pmu \wedge d \Xmu + \nabla \Pimu \wedge \nabla \Etamu + \frac 12 dx^{\mu } \wedge dx^{\nu } \Curv {\mu }{\nu }{\kappa }{\lambda }\eta ^{\kappa }\pi _{\lambda }, \end {equation} | \begin{equation*} d p _ { \mu } \wedge d x ^ { \mu } + \nabla \pi _ { \mu } \wedge \nabla \eta ^ { \mu } + \frac { 1 } { 2 } d x ^ { \mu } \wedge d x ^ { \nu } R _ { \mu \nu \kappa } { } ^ { \lambda } \eta ^ { \kappa } \pi _ { \lambda } , \end{equation*} | 0001015_page004 | isolated |
|
\begin {eqnarray}\DDmu \psi (x,\eta ) = \Dmu \psi (x,\eta ) + \Gam {\mu }{\nu }{\lambda } \eta ^{\nu } \frac {\partial }{\partial \eta ^{\lambda }}\psi (x,\eta ). \end {eqnarray} | \begin{equation*} \nabla _ { \mu } \psi ( x , \eta ) = \partial _ { \mu } \psi ( x , \eta ) + \Gamma _ { \mu \nu } ^ { \lambda } \eta ^ { \nu } \frac { \partial } { \partial \eta ^ { \lambda } } \psi ( x , \eta ) . \end{equation*} | 0001015_page004 | isolated |
|
\begin {eqnarray}H_g &=& i( Q \chi + \chi Q) \End &=& d \delta + \delta d + g^{\mu \nu }\Omu \omega _{\nu } -i (\Pimu \eta ^{\nu } - \eta ^{\nu }\Pimu ) \frac {\partial ^2 h }{\partial \Xmu \partial x_{\nu }}. \end {eqnarray} | \begin{align*} H _ { g } & = & i ( Q \chi + \chi Q ) \\ & = & d \delta + \delta d + g ^ { \mu \nu } \omega _ { \mu } \omega _ { \nu } - i ( \pi _ { \mu } \eta ^ { \nu } - \eta ^ { \nu } \pi _ { \mu } ) \frac { \partial ^ { 2 } h } { \partial x ^ { \mu } \partial x _ { \nu } } . \end{align*} | 0001015_page004 | isolated |
|
$H_g$ | $ H _ { g } $ | 0001015_page005 | embedded |
|
$x_t,\eta _t$ | $ x _ { t } , \eta _ { t } $ | 0001015_page005 | embedded |
|
$SM$ | $ S M $ | 0001015_page005 | embedded |
|
$\Xmu ,\Etamu $ | $ x ^ { \mu } , \eta ^ { \mu } $ | 0001015_page005 | embedded |
|
$b_t$ | $ b _ { t } $ | 0001015_page005 | embedded |
|
$(\theta _t,\rho _t)$ | $ ( \theta _ { t } , \rho _ { t } ) $ | 0001015_page005 | embedded |
|
$(d+ \delta )^2$ | $ ( d + \delta ) ^ { 2 } $ | 0001015_page005 | embedded |
|
$J$ | $ J $ | 0001015_page005 | embedded |
|
$u:\Sigma \to M$ | $ u : \Sigma \rightarrow M $ | 0001015_page005 | embedded |
|
$\Sigma $ | $ \Sigma $ | 0001015_page005 | embedded |
|
$2m$ | $ 2 m $ | 0001015_page005 | embedded |
|
$M$ | $ M $ | 0001015_page005 | embedded |
|
$H^{\alpha }_{\mu }$ | $ H _ { \mu } ^ { \alpha } $ | 0001015_page005 | embedded |
|
$\Etamu $ | $ \eta ^ { \mu } $ | 0001015_page005 | embedded |
|
$\pi ^{\alpha }_{\mu }$ | $ \pi _ { \mu } ^ { \alpha } $ | 0001015_page005 | embedded |
|
$\alpha =1,2$ | $ \alpha = 1 , 2 $ | 0001015_page005 | embedded |
|
$\Sigma $ | $ \Sigma $ | 0001015_page005 | embedded |
|
$\mu =1,\dots ,2 m$ | $ \mu = 1 , \ldots , 2 m $ | 0001015_page005 | embedded |
|
$M$ | $ M $ | 0001015_page005 | embedded |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.