Nöther’s theorems: a study

Acevedo O.A.; Pimentel B.M. · Revista Brasileira de Ensino de Fisica (2023) · DOI: 10.1590/1806-9126-rbef-2023-0091

Resumen

In this paper, we make a complete revision about Nöther’s theorems: The one which refers to the global symmetries, the theorem referring to the local ones, and the corresponding reciprocal theorems. We exemplify these theorems by applying them to a variety of situations. Particularly, we show, through the example of Kepler’s problem, that the first reciprocal Nöther’s theorem finds its maximal applicability only in the Hamiltonian formalism in which the dynamical symmetries are realizable. Finally, we expose the relation between Nöther’s energy-momentum tensor and the metric one. We complement the information by treating, in appendix, Lévy-Leblond–Jackiw’s formulation that intends to unify the two theorems. © Sociedade Brasileira de Física. Printed in Brazil.

Instituciones: Universidad Nacional de Ingeniería