Classical gauge principle -- From field theories to classical mechanics

Abstract

In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the action of a matrix Lie group of transformations parametrized by arbitrary functions. It is formally presented how this property can be introduced in such systems, followed by modern applications. Furthermore, Lagrangians describing classical-mechanics systems with local invariance are separated in equivalence classes according to their local structures.

20 pages, no figures. Expanded version, added references and misprint corrections

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• Reconstruction of higher stage first class constraints into the secondary ones
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• Non-Grassmann mechanical model of the Dirac equation
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Cited by in corpus (1)

• General Solution and Canonical Quantization of the Conic Path Constrained Second-Class System