Geometry of the physical phase space in quantum gauge models

TL;DR

This paper investigates the non-Euclidean geometry of the physical phase space in quantum gauge models, proposing modifications to the Hamiltonian path integral to account for geometric effects and addressing the Gribov problem.

Contribution

It introduces a necessary modification to the Hamiltonian path integral in gauge theories to incorporate the non-Euclidean geometry of the physical phase space.

Findings

Modified path integral resolves Gribov obstruction

Application to lattice gauge theory demonstrates effectiveness

Provides accessible examples for non-specialists

Abstract

The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac gauge invariant states is used to derive a necessary modification of the Hamiltonian path integral in gauge theories of the Yang-Mills type with fermions that takes into account the non-Euclidean geometry of the physical phase space. The new path integral is applied to resolve the Gribov obstruction. Applications to the Kogut-Susskind lattice gauge theory are given. The basic ideas are illustrated with examples accessible for non-specialists.