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Classical Gauge Principle - From Field Theories to Classical Mechanics

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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 parameterized 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.

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Notes

  1. The Zitterbewegung is a trembling motion the free electron would experience. It was first predicted by Schrödinger when analyzing the Dirac equation [45].

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Acknowledgements

BFR would like to thank G. Caetano for indicating valuable references concerning the analogy between non-Abelian gauge theories and general relativity.

Funding

This work was supported by grant #2021/09311-5, São Paulo Research Foundation (FAPESP) and Programa Institucional de Bolsas de Iniciação Científica - XXIX PIBIC/CNPq/UFJF - 2020/2021, project number ID47862. GFVJr was a CNPq/Brazil fellow during the first months of production of this work.

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  1. Bruno F. Rizzuti

    Present address: Departamento de Física, Universidade Federal de Juiz de Fora, José Lourenço Kelmer St., Juiz de Fora, 36036-900, MG, Brazil

  2. Guilherme F. Vasconcelos Jr. and Bruno F. Rizzuti equally contributed to this work.

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  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Matão St., São Paulo, 05508-090, SP, Brazil

    Guilherme F. Vasconcelos Jr.

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Correspondence to Guilherme F. Vasconcelos Jr..

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Rizzuti, B.F., Vasconcelos, G.F. Classical Gauge Principle - From Field Theories to Classical Mechanics. Braz J Phys 52, 63 (2022). https://doi.org/10.1007/s13538-022-01070-2

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