Coordinate-free derivation of Yang-Mills-Chern-Simons field equations

TL;DR

This paper presents a coordinate-free derivation of Yang-Mills-Chern-Simons field equations, revealing their eigenvalue structure related to the covariant laplacian, enhancing theoretical understanding of gauge field dynamics.

Contribution

It introduces a coordinate-free method to derive Yang-Mills-Chern-Simons equations, highlighting their eigenvalue form and advancing the theoretical framework.

Findings

Derived field equations as eigenvalue equations for the covariant laplacian.

Provided a coordinate-free formulation of gauge field equations.

Enhanced understanding of the mathematical structure of Yang-Mills-Chern-Simons theories.

Abstract

In this paper we derive in a coordinate-free manner the field equations for a lagrangean consisting of Yang-Mills kinetical term plus Chern-Simons self-coupling term. This equation turns out to be an eigenvalue equation for the covariant laplacian.