Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism

The unfree gauge symmetry implies that gauge variation of the action functional vanishes provided for the gauge parameters are restricted by the differential equations. The unfree gauge symmetry is shown to lead to the global conserved quantities whose on shell values are defined by the asymptotics...

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Autores principales:	V.A. Abakumova, I.Yu. Karataeva, S.L. Lyakhovich
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/68b8b52b9c374f56a686ca00f4c15799
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spelling	oai:doaj.org-article:68b8b52b9c374f56a686ca00f4c157992021-12-04T04:32:50ZReducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism0550-321310.1016/j.nuclphysb.2021.115577https://doaj.org/article/68b8b52b9c374f56a686ca00f4c157992021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S0550321321002741https://doaj.org/toc/0550-3213The unfree gauge symmetry implies that gauge variation of the action functional vanishes provided for the gauge parameters are restricted by the differential equations. The unfree gauge symmetry is shown to lead to the global conserved quantities whose on shell values are defined by the asymptotics of the fields or data on the lower dimension surface, or even at the point of the space-time, rather than Cauchy hyper-surface. The most known example of such quantity is the cosmological constant of unimodular gravity. More examples are provided in the article for the higher spin gravity analogues of the cosmological constant. Any action enjoying the unfree gauge symmetry is demonstrated to admit the alternative form of gauge symmetry with the higher order derivatives of unrestricted gauge parameters. The higher order gauge symmetry is reducible in general, even if the unfree symmetry is not. The relationship is detailed between these two forms of gauge symmetry in the constrained Hamiltonian formalism. The local map is shown to exist from the unfree gauge algebra to the reducible higher order one, while the inverse map is non-local, in general. The Hamiltonian BFV-BRST formalism is studied for both forms of the gauge symmetry. These two Hamiltonian formalisms are shown connected by canonical transformation involving the ghosts. The generating function is local for the transformation, though the transformation as such is not local, in general. Hence, these two local BRST complexes are not quasi-isomorphic in the sense that their local BRST-cohomology groups can be different. This difference in particular concerns the global conserved quantities. From the standpoint of the BRST complex for unfree gauge symmetry, these quantities are BRST-exact, while for the alternative complex, these quantities are the non-trivial co-cycles.V.A. AbakumovaI.Yu. KarataevaS.L. LyakhovichElsevierarticleNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENNuclear Physics B, Vol 973, Iss , Pp 115577- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 V.A. Abakumova I.Yu. Karataeva S.L. Lyakhovich Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism
description	The unfree gauge symmetry implies that gauge variation of the action functional vanishes provided for the gauge parameters are restricted by the differential equations. The unfree gauge symmetry is shown to lead to the global conserved quantities whose on shell values are defined by the asymptotics of the fields or data on the lower dimension surface, or even at the point of the space-time, rather than Cauchy hyper-surface. The most known example of such quantity is the cosmological constant of unimodular gravity. More examples are provided in the article for the higher spin gravity analogues of the cosmological constant. Any action enjoying the unfree gauge symmetry is demonstrated to admit the alternative form of gauge symmetry with the higher order derivatives of unrestricted gauge parameters. The higher order gauge symmetry is reducible in general, even if the unfree symmetry is not. The relationship is detailed between these two forms of gauge symmetry in the constrained Hamiltonian formalism. The local map is shown to exist from the unfree gauge algebra to the reducible higher order one, while the inverse map is non-local, in general. The Hamiltonian BFV-BRST formalism is studied for both forms of the gauge symmetry. These two Hamiltonian formalisms are shown connected by canonical transformation involving the ghosts. The generating function is local for the transformation, though the transformation as such is not local, in general. Hence, these two local BRST complexes are not quasi-isomorphic in the sense that their local BRST-cohomology groups can be different. This difference in particular concerns the global conserved quantities. From the standpoint of the BRST complex for unfree gauge symmetry, these quantities are BRST-exact, while for the alternative complex, these quantities are the non-trivial co-cycles.
format	article
author	V.A. Abakumova I.Yu. Karataeva S.L. Lyakhovich
author_facet	V.A. Abakumova I.Yu. Karataeva S.L. Lyakhovich
author_sort	V.A. Abakumova
title	Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism
title_short	Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism
title_full	Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism
title_fullStr	Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism
title_full_unstemmed	Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism
title_sort	reducible gauge symmetry versus unfree gauge symmetry in hamiltonian formalism
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/68b8b52b9c374f56a686ca00f4c15799
work_keys_str_mv	AT vaabakumova reduciblegaugesymmetryversusunfreegaugesymmetryinhamiltonianformalism AT iyukarataeva reduciblegaugesymmetryversusunfreegaugesymmetryinhamiltonianformalism AT sllyakhovich reduciblegaugesymmetryversusunfreegaugesymmetryinhamiltonianformalism
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Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism

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