Chern-Simons states and topologically massive gauge theories

Abstract

In an abelian topologically massive gauge theory, any eigenstate of the Hamiltonian can be decomposed into a factor describing massive propagating gauge bosons and a Chern-Simons wave function describing a set of nonpropagating "topological" excitations. The energy depends only on the propagating modes, and energy eigenstates thus occur with a degeneracy that can be parametrized by the Hilbert space of the pure Chern-Simons theory. We show that for a nonabelian topologically massive gauge theory, this degeneracy is lifted: although the Gauss law constraint can be solved with a similar factorization, the Hamiltonian couples the propagating and nonpropagating (topological) modes. *

Radiative processes as a condensation phenomenon and the physical meaning of deformed canonical structures

“…It is very interesting and highly nontrivial that this separation is possible. It means, for example, that the energy propagating modes is given entirely by the SD sector in (9) but the energy eigenstates have a degeneracy parameterized by the Hilbert space of pure Chern-Simons theory (a topological degeneracy) [16]. In this way we establish the MCS-SD dynamical duality connection depicted in the diagram (3).…”

A Immirzi-like parameter for 3D quantum gravity

“…π) is a connection while a functional derivative should transform covariantly under a gauge transformation. Then the quantization of the Gauss constraint implies to work with states which are not exactly gauge invariant [15]. When dealing with a background independent theory such as 3d gravity, the loop quantization avoids those difficulties and provides a well-defined gauge invariant and diff-invariant state space.…”

Renormalization Ambiguities and Gauge Symmetry in Chern–simons Theories

“…3 The quantum states of the non-Abelian Chern-Simons theory are related with the conformal blocks of the two-dimensional Wess-Zumino-Witten model. 4,5 There is a connection between the Wilson loops of the Chern-Simons theory and the topological invariants (polynomial invariants of links and knots) of three-dimensional surfaces. [6][7][8] The Chern-Simons theory is exactly solvable in the canonical formalism, but some of the above aspects of the theory must be formulated in the covariant formalism.…”