Generalization of the Noether Theorem: Global and Local Symmetries, Dynamical Functionals and Boundary Conditions

Fiziev, Plamen

doi:10.3390/proceedings2010043

Open AccessAbstract

Generalization of the Noether Theorem: Global and Local Symmetries, Dynamical Functionals and Boundary Conditions^†

by

Plamen Fiziev

^1,2

¹

Joint Institute for Nuclear Research (JINR), 141980 Dubna, Russia

²

Foundation of Theoretical and Computational Physics and Astrophysics, Sofia 1164, Bulgaria

^†

Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017.

Proceedings 2018, 2(1), 43; https://doi.org/10.3390/proceedings2010043

Published: 4 January 2018

(This article belongs to the Proceedings of The First International Conference on Symmetry)

Download Versions Notes

Abstract

:

We consider the most general form of the Noether theorem which is suitable for the treatment of global symmetries, described by symmetry-groups, and local symmetries, described by symmetry-algebras, which may not be integrable to symmetry groups. The principle new notion is specific dynamical functionals which solve the problem by replacing the standard action functionals. We also discuss the compatibility of the boundary conditions and the corresponding variational principles. Many illustrative examples are shown.

© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Share and Cite

MDPI and ACS Style

Fiziev, P. Generalization of the Noether Theorem: Global and Local Symmetries, Dynamical Functionals and Boundary Conditions. Proceedings 2018, 2, 43. https://doi.org/10.3390/proceedings2010043

AMA Style

Fiziev P. Generalization of the Noether Theorem: Global and Local Symmetries, Dynamical Functionals and Boundary Conditions. Proceedings. 2018; 2(1):43. https://doi.org/10.3390/proceedings2010043

Chicago/Turabian Style

Fiziev, Plamen. 2018. "Generalization of the Noether Theorem: Global and Local Symmetries, Dynamical Functionals and Boundary Conditions" Proceedings 2, no. 1: 43. https://doi.org/10.3390/proceedings2010043

APA Style

Fiziev, P. (2018). Generalization of the Noether Theorem: Global and Local Symmetries, Dynamical Functionals and Boundary Conditions. Proceedings, 2(1), 43. https://doi.org/10.3390/proceedings2010043

Article Menu

Generalization of the Noether Theorem: Global and Local Symmetries, Dynamical Functionals and Boundary Conditions^†

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI

Article Menu

Generalization of the Noether Theorem: Global and Local Symmetries, Dynamical Functionals and Boundary Conditions †

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI

Generalization of the Noether Theorem: Global and Local Symmetries, Dynamical Functionals and Boundary Conditions^†