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

Abstract

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