Phase space structure and the path integral for gauge theories on a cylinder

TL;DR

This paper characterizes the phase space of gauge theories on a cylindrical spacetime, introduces a path integral formulation that addresses Gribov's problem, and discusses implications for fermion quantum dynamics.

Contribution

It provides a novel description of the gauge theory phase space as a quotient by the affine Weyl group and proposes a path integral approach that naturally solves Gribov's problem.

Findings

Phase space is the quotient ${\bf R}^{2r}/W_A$ for gauge theories on a cylinder.

Path integral formula involves symmetrization over the affine Weyl group.

Addresses nontrivial phase space effects on fermion quantum dynamics.

Abstract

The physical phase space of gauge field theories on a cylindrical spacetime with an arbitrary compact simple gauge group is shown to be the quotient $ {\bf R}^{2r}/W_A, $ $ r $ a rank of the gauge group, $ W_A $ the affine Weyl group. The PI formula resulting from Dirac's operator method contains a symmetrization with respect to $ W_A $ rather than the integration domain reduction. It gives a natural solution to Gribov's problem. Some features of fermion quantum dynamics caused by the nontrivial phase space geometry are briefly discussed.