A proposal for the Yang-Mills vacuum and mass gap

TL;DR

This paper explores a novel approach to understanding the Yang-Mills vacuum and mass gap by analyzing Feynman rules, effective actions, and vacuum properties, aiming to address confinement and the strong-CP problem in gauge theories.

Contribution

It proposes a new set of Feynman rules and effective actions that incorporate Gauss's law constraints, providing insights into the vacuum structure and mass gap in Yang-Mills theories.

Findings

Identifies solutions for the Lagrangian and Hamiltonian equations of motion.

Discusses the stability of these solutions in Minkowski space.

Explores the properties of confining and perturbative vacua and their transitions.

Abstract

I examine a set of Feynman rules, and the resulting effective action, that were proposed in order to incorporate the constraint of Gauss's law in the perturbation expansion of gauge field theories. A set of solutions for the Lagrangian and Hamiltonian equations of motion in Minkowski space-time, as well as their stability, are investigated. A discussion of the Euclidean action, confinement, and the strong-CP problem is also included. The properties and symmetries of the perturbative and the confining vacuum are explored, as well as the possible transitions between them, and the relations with phenomenological models of the strong interactions.