  We study the infra-red limit of non-abelian Chern-Simons gauge theory
perturbed by a non-topological, albeit gauge invariant, mass term. It is shown
that, in this limit, we may construct an infinite class of integrable quantum
mechanical models which, for the case of SU(2) group, are labelled by the
angular momentum eigenvalue. The first non-trivial example in this class is
obtained for the triplet representation and it physically describes the gauge
invariant coupling of a non-abelian Chern-Simons particle with a particle
moving on $S^3$ - the SU(2) group manifold. In addition to this, the model has
a fascinating resemblance to the Landau problem and may be regarded as a
non-abelian and a non-linear generalisation of the same defined on the
three-sphere with the uniform magnetic field replaced by an angular momentum
field. We explicitly solve for some eigenstates of this model in a closed form
in terms of some generalised orthogonal polynomials. In the process, we unravel
some startling connections with Anderson's chain models which are important in
the study of disordered systems in condensed matter physics. We also sketch a
method which allows us, in principle, to find the energy eigenvalues
corresponding to the above eigenstates of the theory if the Lyapunov exponents
of the transfer matrix of the infinite chain model involved are known.

High Energy Physics - Theory