Constant solutions of Yang-Mills equations and generalized Proca equations

TL;DR

This paper introduces Yang-Mills-Proca equations, a non-gauge-invariant generalization of Proca and Yang-Mills equations, and explores their constant solutions across various Lie algebras, including Clifford and Grassmann algebras.

Contribution

It presents new generalized equations and analyzes their constant solutions for arbitrary Lie algebras, including specific cases like Clifford and Grassmann algebras.

Findings

Identified constant solutions for the generalized equations.

Analyzed perturbation series near constant solutions.

Extended solutions to specific Lie algebra cases.

Abstract

In this paper we present some new equations which we call Yang-Mills-Proca equations (or generalized Proca equations). This system of equations is a generalization of Proca equation and Yang-Mills equations and it is not gauge invariant. We present a number of constant solutions of this system of equations in the case of arbitrary Lie algebra. In details we consider the case when this Lie algebra is Clifford algebra or Grassmann algebra. We consider solutions of Yang-Mills equations in the form of perturbation theory series near the constant solution.