Functional Approach to Classical Yang-Mills Theories

TL;DR

This paper extends the functional operatorial approach from classical mechanics to classical Yang-Mills theories, addressing gauge-fixing and Faddeev-Popov determinants within this formalism.

Contribution

It introduces a novel functional framework for classical Yang-Mills theories, incorporating gauge-fixing and Faddeev-Popov determinants.

Findings

Functional approach successfully applied to classical Yang-Mills theories

Gauge-fixing and Faddeev-Popov determinants naturally emerge in the formalism

Provides a new perspective on classical field theory quantization methods

Abstract

Sometime ago it was shown that the operatorial approach to classical mechanics, pioneered in the 30's by Koopman and von Neumann, can have a functional version. In this talk we will extend this functional approach to the case of classical field theories and in particular to the Yang-Mills ones. We shall show that the issues of gauge-fixing and Faddeev-Popov determinant arise also in this classical formalism.