Polyakov's Spin Factor for a Classical Spinning Particle via BRST Invariant Path Integral

TL;DR

This paper derives the propagator and spin factor for a classical massive spinning particle using a BRST invariant path integral approach, addressing reparametrization and quasi-supersymmetry constraints.

Contribution

It introduces a BRST invariant path integral formulation for a classical spinning particle, reproducing the spin factor consistent with pseudo-classical methods.

Findings

Derived the propagator for a classical massive spinning particle.

Established the spin factor within a BRST invariant framework.

Connected reparametrization invariance and quasi-supersymmetry in the path integral.

Abstract

For the `classical' formulation of a massive spinning particle, the propagator is obtained along with the spin factor. We treat the system with two kinds of constraints that were recently shown to be concerned with the reparametrization invariance and `quasi-supersymmetry'. In the path integral, the BRST invariant Lagrangian is used and the same spin factor is obtained as in the pseudo-classical formulation.