Group Quantization on Configuration Space: Gauge Symmetries and Linear Fields

TL;DR

This paper develops a configuration-space approach to group quantization, extending the GAQ formalism to include gauge symmetries and linear fields, and applies it to quantize abelian Chern-Simons models on closed surfaces.

Contribution

It introduces a comprehensive, systematic framework for group quantization with gauge symmetries, specifically tailored for linear fields and abelian current groups.

Findings

Systematic analysis of gauge symmetries in group quantization.

Quantization of abelian Chern-Simons models on arbitrary closed surfaces.

Extension of the GAQ formalism to configuration space.

Abstract

A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous, algebraic generalization. This presentation serves to make a comprehensive discussion in which other extensions of the formalism, particularly to incorporate gauge symmetries, are developed as well. Both images are combined in order to analyse, in a systematic manner and with complete generality, the case of linear fields (abelian current groups). To ilustrate these developments we particularize them for several fields and, in particular, we carry out the quantization of the abelian Chern-Simons models over an arbitrary closed surface in detail.