Covariantly Quantized Spinning Particle and its Possible Connection to Non-Commutative Space-Time

TL;DR

This paper explores covariant quantization of a spinning particle in 2+1 dimensions, addressing reducibility issues in constraints and connecting non-commutative space-time with conventional models through BRST and Batalin-Tyutin methods.

Contribution

It presents a detailed analysis of covariant quantization methods for the spinning particle, including handling reducible constraints and establishing links to non-commutative space-time.

Findings

Successful covariant quantization of the model using Batalin-Tyutin method.

Established a mapping between non-commutative and ordinary space-time.

Discussed BRST quantization in the context of reducible constraints.

Abstract

Covariant quantization of the Nambu-Goto spinning particle in 2+1-dimensions is studied. The model is relevant in the context of recent activities in non-commutative space-time. From a technical point of view also covariant quantization of the model poses an interesting problem: the set of second class constraints (in the Dirac classification scheme) is {\it reducible}. The reducibility problem is analyzed from two contrasting approaches: (i) the auxiliary variable method [bn] and (ii) the projection operator method [blm]. Finally in the former scheme, a Batalin-Tyutin quantization has been done. This induces a mapping between the non-commutative and the ordinary space-time. BRST quantization programme in the latter scheme has also been discussed.