Weinberg propagator of a free massive particle with an arbitrary spin from the BFV-BRST path integral

TL;DR

This paper derives the Weinberg propagator for a free massive particle with arbitrary spin using the BFV-BRST path integral approach, emphasizing boundary conditions' role in particle-antiparticle representation.

Contribution

It presents a novel derivation of the Weinberg propagator in an index-free form via the BFV-BRST path integral for particles of arbitrary spin.

Findings

Derived the Weinberg propagator in index-free form

Showed boundary conditions determine particle/antiparticle representation

No renormalization of the path integral measure was needed

Abstract

The transition amplitude is obtained for a free massive particle of arbitrary spin by calculating the path integral in the index-spinor formulation within the BFV-BRST approach. None renormalizations of the path integral measure were applied. The calculation has given the Weinberg propagator written in the index-free form with the use of index spinor. The choice of boundary conditions on the index spinor determines holomorphic or antiholomorphic representation for the canonical description of particle/antiparticle spin.