Disorder parameter and canonical quantization approach in lattice gauge theory

TL;DR

This paper derives a functional integral representation of the disorder parameter in lattice gauge theory, addressing issues related to modified actions, boundary conditions, and gauge fixing.

Contribution

It provides a rigorous derivation of the functional integral form of the disorder parameter, clarifying boundary conditions and gauge fixing in lattice gauge theory.

Findings

Resolved the problem of choosing modified actions

Clarified boundary condition selection along the time direction

Discussed gauge fixing in the functional integral context

Abstract

The work is dedicated to the derivation of the 'functional' integral representation of the disorder parameter. This derivation resolves the problem of the choice of the so called modifed action as well as the problem of the choice of the boundary conditions along the 'time' direction. The question of the gauge fixing in the functional integral representation is also discussed.