Maxwell Chern Simons Theory in a Geometric Representation

TL;DR

This paper presents a geometric quantization of Maxwell Chern Simons theory, revealing its equivalence to a massless scalar field with topological interactions, and connecting it to particle quantum mechanics with Chern Simons fields.

Contribution

It introduces a generalized geometric representation for Maxwell Chern Simons theory, extending the Abelian Loop Representation and highlighting its topological and multivalued wave functional features.

Findings

Wave functional is multivalued due to topological interaction

Maxwell Chern Simons theory maps to a massless scalar field

Connection established with quantum particle mechanics involving Chern Simons fields

Abstract

We quantize the Maxwell Chern Simons theory in a geometric representation that generalizes the Abelian Loop Representation of Maxwell theory. We find that in the physical sector, the model can be seen as the theory of a massles scalar field with a topological interaction that enforces the wave functional to be multivalued. This feature allows to relate the Maxwell Chern Simons theory with the quantum mechanics of particles interacting through a Chern Simons field