Canonical Quantization and Topological Theories

TL;DR

This paper discusses the canonical quantization of topological particles, linking BRST quantization to supersymmetric quantum mechanics and exploring extensions to higher-dimensional models.

Contribution

It demonstrates how BRST quantization of topological particles relates to supersymmetric quantum mechanics and discusses rigorous path integral methods and potential extensions.

Findings

BRST quantization yields supersymmetric quantum mechanics

Rigorous path integral methods are discussed

Extensions to 2D models are considered

Abstract

The canonical quantization of the topological particle is described; it is shown that BRST quantization of the model gives the supersymmetric quantum mechanical model considered by Witten when investigating Morse theory, and the rigorous path integral method appropriate for this model is discussed. Possibilities for the extension of this work to two dimensional models are briefly considered.