Physics – Classical Physics
Scientific paper
2009-07-14
Am.J.Phys.77:839-843,2009
Physics
Classical Physics
12 pages, 0 figures. This article has been accepted by the American Journal of Physics Replacement corrects two typos referenc
Scientific paper
10.1119/1.3153503
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.
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