Operator Algebra in Chern-Simons Theory on a Torus

TL;DR

This paper explores the operator algebra structure in Chern-Simons theory on a torus, analyzing the commutation relations of Hamiltonian and momenta, and examining the implications for physical states and vacua.

Contribution

It provides a detailed analysis of the operator algebra and state degeneracies in Chern-Simons theory with matter on a torus, highlighting conditions for commutation.

Findings

Hamiltonian and momenta commute only in the physical Hilbert space

Degenerate physical states and vacua are related through the operator algebra

Multicomponent Schrödinger wavefunctions arise in the theory

Abstract

We consider Chern-Simons gauge theory on a torus with both nonrelativistic and relativistic matter. It is shown that the Hamiltonian and two total momenta commute among themselves only in the physical Hilbert space. We also discuss relations among degenerate physical states, degenerate vacua, and the existence of multicomponent Schrodinger wavefunctions.