A pedagogical introduction to the Slavnov formulation of quantum Yang-Mills theory

TL;DR

This paper provides a detailed pedagogical introduction to Slavnov's formulation of quantum Yang-Mills theory, emphasizing its gauge and Lorentz invariance, with potential extensions to quantum gravity.

Contribution

It offers a comprehensive explanation of Slavnov's approach, including calculations of the functional integral and gauge invariance, which were not previously detailed in the literature.

Findings

Demonstrates invariance of the S-matrix under shifted gauge transformations

Details the functional integral calculations for the Yang-Mills theory

Discusses potential extension to quantum gravity in Prentki gauge

Abstract

Over the last few years, Slavnov has proposed a formulation of quantum Yang-Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the ghost field Lagrangian. This paper presents in detail some of the necessary calculations, i.e. those dealing with the functional integral for the S-matrix and its invariance under shifted gauge transformations. The extension of this formalism to quantum gravity in the Prentki gauge deserves consideration.