The relativistic top: An application of the BFV quantization procedure for systems with degenerate constraints

TL;DR

This paper applies the BFV quantization method to the relativistic top, a system with degenerate constraints, demonstrating how different gauge choices lead to equivalent constraint formulations in the Hamiltonian formalism.

Contribution

It introduces a novel application of the BFV quantization procedure to the relativistic top with second class constraints, converting them into first class constraints for path integral quantization.

Findings

Different gauge choices yield equivalent forms of the constraints.

The BFV method successfully quantizes the relativistic top system.

Constraints can be systematically modified for quantization.

Abstract

The physical phase space of the relativistic top, as defined by Hanson and Regge, is expressed in terms of canonical coordinates of the Poincar\'e group manifold. The system is described in the Hamiltonian formalism by the mass shell condition and constraints that reduce the number of spin degrees of freedom. The constraints are second class and are modified into a set of first class constraints by adding combinations of gauge fixing functions. The Batalin-Fradkin-Vilkovisky (BFV) method is then applied to quantize the system in the path integral formalism in Hamiltonian form. It is finally shown that different gauge choices produce different equivalent forms of the constraints.