Pseudoclassical description of scalar particle in non-Abelian background and path-integral representations

TL;DR

This paper develops path-integral representations and pseudoclassical actions for scalar particles in non-Abelian backgrounds, generalizing previous methods to arbitrary SU(N) representations using antisymmetric generators and fermionic coherent states.

Contribution

It introduces a generalized path-integral construction for scalar particles in non-Abelian fields applicable to any SU(N) representation, including an alternative fermionic coherent state approach.

Findings

Derived path-integral representations for scalar propagators in non-Abelian backgrounds.

Constructed pseudoclassical actions and verified their consistency through classical analysis and quantization.

Extended the methodology to arbitrary SU(N) representations using antisymmetric generators and fermionic states.

Abstract

Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman 1993 of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then quantized to prove their consistency.