## Journal of Geometry and Symmetry in Physics

- J. Geom. Symmetry Phys.
- Volume 42 (2016), 53-72.

### Constant Solutions of Yang-Mills Equations and Generalized Proca Equations

Nikolay Marchuk and Dmitry Shirokov

#### Abstract

Here 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. We consider in detail the case when this Lie algebra is a Clifford or a Grassmann algebra and derive solutions of Yang-Mills equations in the form of perturbation theory series near the constant solution.

#### Article information

**Source**

J. Geom. Symmetry Phys., Volume 42 (2016), 53-72.

**Dates**

First available in Project Euclid: 31 May 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.jgsp/1496196023

**Digital Object Identifier**

doi:10.7546/jgsp-42-2016-53-72

**Mathematical Reviews number (MathSciNet)**

MR3586443

**Zentralblatt MATH identifier**

1366.35152

#### Citation

Marchuk, Nikolay; Shirokov, Dmitry. Constant Solutions of Yang-Mills Equations and Generalized Proca Equations. J. Geom. Symmetry Phys. 42 (2016), 53--72. doi:10.7546/jgsp-42-2016-53-72. https://projecteuclid.org/euclid.jgsp/1496196023