Extensions of Noether's Second Theorem: from continuous to discrete systems
Mathematical Physics
2015-05-27 v1 math.MP
Abstract
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational problem whose symmetries depend upon a set of free or partly-constrained functions. Our approach extends further to deal with finite difference systems. The results are easy to apply; several well-known continuous and discrete systems are used as illustrations.
Cite
@article{arxiv.1103.3267,
title = {Extensions of Noether's Second Theorem: from continuous to discrete systems},
author = {Peter E. Hydon and Elizabeth L. Mansfield},
journal= {arXiv preprint arXiv:1103.3267},
year = {2015}
}