Explicit gauge covariant Euler-Lagrange equation

Abstract

The application of a gauge covariant derivative to the Euler-Lagrange equation yields a shortcut to the equations of motion for a field subject to an external force. The gauge covariant derivative includes an external force as an intrinsic part of the derivative and hence simplifies Lagrangians containing tensor and gauge covariant fields. The gauge covariant derivative used in the covariant Euler-Lagrange equation is presented as an extension of the coordinate covariant derivative used in tensor analysis. Several examples provide useful demonstrations of the covariant derivative relevant to studies in general relativity and gauge theory.

12 pages, 0 figures. This article has been accepted by the American Journal of Physics Replacement corrects two typos referencing Section Roman numerals

Cited by in corpus (5)

• Gauge-covariant canonical formalism revisited with application to the proton spin decomposition
• Cosmic Expansion via Axion-Induced Quintessence
• A mechanical analog of Bohr's atom based on de Broglie's double-solution approach
• Varying without varying: Reparameterisations, Diffeomorphisms, General Covariance, Lie derivatives, and all that
• The Emergence of Superconducting Systems in Anti-de Sitter Space