The Physical Projector and Topological Quantum Field Theories: U(1) Chern-Simons Theory in 2+1 Dimensions

TL;DR

This paper applies the physical projector method to U(1) Chern-Simons theory in 2+1 dimensions, demonstrating how it isolates gauge-invariant physical states based on the manifold's topology.

Contribution

It introduces and applies the physical projector approach to a topological quantum field theory, providing explicit construction and analysis of physical states.

Findings

Physical projector effectively reduces degrees of freedom

Physical states determined by manifold topology

Method applicable to gauge-invariant systems

Abstract

The recently proposed physical projector approach to the quantisation of gauge invariant systems is applied to the U(1) Chern-Simons theory in 2+1 dimensions as one of the simplest examples of a topological quantum field theory. The physical projector is explicitely demonstrated to be capable of effecting the required projection from the initially infinite number of degrees of freedom to the finite set of gauge invariant physical states whose properties are determined by the topology of the underlying manifold.