Chern-Simons States and Topologically Massive Gauge Theories

TL;DR

This paper explores the structure of eigenstates in abelian and nonabelian topologically massive gauge theories, revealing how topological and propagating modes interact and differ in degeneracy and coupling.

Contribution

It demonstrates the factorization of eigenstates in abelian theories and analyzes how nonabelian theories couple topological and propagating modes, lifting degeneracy.

Findings

Eigenstates in abelian theories factor into massive and topological parts.

Degeneracy in abelian theories depends on Chern-Simons Hilbert space.

In nonabelian theories, the coupling lifts the degeneracy.

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 {\em 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.