Classical gauge theories as systems with constraints: a geometric point of view

TL;DR

This paper reviews the Hamiltonian formulation of constrained classical systems, clarifying the geometric nature of classical gauge theories, and provides a translation of a previous work for broader accessibility.

Contribution

It offers a geometric perspective on gauge theories through Hamiltonian constraints, translating prior work into English for wider dissemination.

Findings

Clarifies the geometric interpretation of gauge theories

Highlights the role of constraints in Hamiltonian systems

Provides a translation of previous foundational work

Abstract

In this paper, we briefly review the Hamiltonian formulation of classical systems that are constrained to submanifolds so that, within this context, the true meaning of classical gauge theories becomes clear. Please note that this paper is nothing more than a near-literal translation of Ref. [1], which we originally published in Brazilian Portuguese in 2018. Therefore, if you, the reader, find this paper useful enough to cite it in any of your works, we kindly ask that you (also) cite Ref. [1].