Approximate Mei Symmetries and Invariants of the Hamiltonian

It is known that corresponding to each Noether symmetry there is a conserved quantity. Another class of symmetries that corresponds to conserved quantities is the class of Mei symmetries. However, the two sets of symmetries may give different conserved quantities. In this paper, a procedure of findi...

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Autores principales:	Umara Kausar, Tooba Feroze
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	approximate Noether symmetries conservation laws Hamiltonian Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0f2c20e89df94a0b9925d86b06925973
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spelling	oai:doaj.org-article:0f2c20e89df94a0b9925d86b069259732021-11-25T18:17:08ZApproximate Mei Symmetries and Invariants of the Hamiltonian10.3390/math92229102227-7390https://doaj.org/article/0f2c20e89df94a0b9925d86b069259732021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2910https://doaj.org/toc/2227-7390It is known that corresponding to each Noether symmetry there is a conserved quantity. Another class of symmetries that corresponds to conserved quantities is the class of Mei symmetries. However, the two sets of symmetries may give different conserved quantities. In this paper, a procedure of finding approximate Mei symmetries and invariants of the perturbed/approximate Hamiltonian is presented that can be used in different fields of study where approximate Hamiltonians are under consideration. The results are presented in the form of theorems along with their proofs. A simple example of mechanics is considered to elaborate the method of finding these symmetries and the related Mei invariants. At the end, a comparison of approximate Mei symmetries and approximate Noether symmetries is also given. The comparison shows that there is only one common symmetry in both sets of symmetries. Hence, rest of the symmetries in the two sets correspond to two different sets of conserved quantities.Umara KausarTooba FerozeMDPI AGarticleapproximate Noether symmetriesconservation lawsHamiltonianMathematicsQA1-939ENMathematics, Vol 9, Iss 2910, p 2910 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	approximate Noether symmetries conservation laws Hamiltonian Mathematics QA1-939
spellingShingle	approximate Noether symmetries conservation laws Hamiltonian Mathematics QA1-939 Umara Kausar Tooba Feroze Approximate Mei Symmetries and Invariants of the Hamiltonian
description	It is known that corresponding to each Noether symmetry there is a conserved quantity. Another class of symmetries that corresponds to conserved quantities is the class of Mei symmetries. However, the two sets of symmetries may give different conserved quantities. In this paper, a procedure of finding approximate Mei symmetries and invariants of the perturbed/approximate Hamiltonian is presented that can be used in different fields of study where approximate Hamiltonians are under consideration. The results are presented in the form of theorems along with their proofs. A simple example of mechanics is considered to elaborate the method of finding these symmetries and the related Mei invariants. At the end, a comparison of approximate Mei symmetries and approximate Noether symmetries is also given. The comparison shows that there is only one common symmetry in both sets of symmetries. Hence, rest of the symmetries in the two sets correspond to two different sets of conserved quantities.
format	article
author	Umara Kausar Tooba Feroze
author_facet	Umara Kausar Tooba Feroze
author_sort	Umara Kausar
title	Approximate Mei Symmetries and Invariants of the Hamiltonian
title_short	Approximate Mei Symmetries and Invariants of the Hamiltonian
title_full	Approximate Mei Symmetries and Invariants of the Hamiltonian
title_fullStr	Approximate Mei Symmetries and Invariants of the Hamiltonian
title_full_unstemmed	Approximate Mei Symmetries and Invariants of the Hamiltonian
title_sort	approximate mei symmetries and invariants of the hamiltonian
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/0f2c20e89df94a0b9925d86b06925973
work_keys_str_mv	AT umarakausar approximatemeisymmetriesandinvariantsofthehamiltonian AT toobaferoze approximatemeisymmetriesandinvariantsofthehamiltonian
_version_	1718411363609477120

Approximate Mei Symmetries and Invariants of the Hamiltonian

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