Pure bosonic worldline path integral representation for fermionic determinants, non-Abelian Stokes theorem, and quasiclassical approximation in QCD

TL;DR

This paper develops a purely bosonic path integral approach for fermionic determinants in QCD, deriving a new non-Abelian Stokes theorem, and applying quasiclassical methods to obtain equations of motion.

Contribution

It introduces a novel bosonic path integral representation for fermionic determinants and Green functions in QCD, along with a new non-Abelian Stokes theorem and quasiclassical equations.

Findings

New bosonic path integral for fermionic determinants

A novel non-Abelian Stokes theorem derived

Quasiclassical equations of motion in QCD obtained

Abstract

Simple bosonic path integral representation for path ordered exponent is derived. This representation is used, at first, to obtain new variant of non-Abelian Stokes theorem. Then new pure bosonic worldline path integral representations for fermionic determinant and Green functions are presented. Finally, applying stationary phase method, we get quasiclassical equations of motion in QCD.