Classical gauge principle -- From field theories to classical mechanics
Mathematical Physics
2022-03-03 v2 math.MP
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.
Keywords
Cite
@article{arxiv.2109.01264,
title = {Classical gauge principle -- From field theories to classical mechanics},
author = {B. F. Rizzuti and G. F. Vasconcelos},
journal= {arXiv preprint arXiv:2109.01264},
year = {2022}
}
Comments
20 pages, no figures. Expanded version, added references and misprint corrections