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

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.