On the evaluation of the evolution operator Z_Reg(R_2,R_1) in the Diakonov-Petrov approach to the Wilson loop

TL;DR

This paper evaluates the evolution operator Z_Reg(R_2,R_1) in the Diakonov-Petrov approach to Wilson loops and finds that it vanishes, challenging previous assumptions about its role.

Contribution

The paper provides a detailed evaluation of the evolution operator in the Diakonov-Petrov framework and demonstrates that it vanishes, offering new insights into the Wilson loop formulation.

Findings

The evolution operator Z_Reg(R_2,R_1) vanishes.

The evaluation uses the original Diakonov-Petrov procedure.

Results impact the understanding of Wilson loop definitions.

Abstract

We evaluate the evolution operator Z_Reg(R_2,R_1) introduced by Diakonov and Petrov for the definition of the Wilson loop in terms of a path integral over gauge degrees of freedom. We use the procedure suggested by Diakonov and Petrov (Phys. Lett. B224 (1989) 131) and show that the evolution operator vanishes.