Spinor and Isospinor Structure of Relativistic Particle Propagators

TL;DR

This paper uses path integral methods to analyze the spinor and isospinor structures of relativistic particle propagators in external fields, providing explicit decompositions and general results for Dirac and scalar particles.

Contribution

It introduces a unified path integral approach to explicitly derive spinor and isospinor structures of propagators in external fields, including Grassmannian integrations and bosonic path integrals.

Findings

Explicit decomposition of Dirac propagator in electromagnetic fields.

General bosonic path integral representation of propagators.

Analysis of isospinor structure in non-Abelian fields.

Abstract

Representations by means of path integrals are used to find spinor and isospinor structure of relativistic particle propagators in external fields. For Dirac propagator in an external electromagnetic field all grassmannian integrations are performed and a general result is presented via a bosonic path integral. The spinor structure of the integrand is given explicitly by its decomposition in the independent $\gamma$-matrix structures. Similar technique is used to get the isospinor structure of the scalar particle propagator in an external non-Abelian field.