Carroll contractions of Lorentz-invariant theories

Abstract We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one “electric” and the other “magnetic”. Each can be obtained from the corresponding Lorentz-invariant theory written in Hamilto...

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Autores principales:	Marc Henneaux, Patricio Salgado-Rebolledo
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Space-Time Symmetries Field Theories in Higher Dimensions Classical Theories of Gravity Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/e9ae0bf9a75946d695608bfe032d198d
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spelling	oai:doaj.org-article:e9ae0bf9a75946d695608bfe032d198d2021-11-28T12:40:27ZCarroll contractions of Lorentz-invariant theories10.1007/JHEP11(2021)1801029-8479https://doaj.org/article/e9ae0bf9a75946d695608bfe032d198d2021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)180https://doaj.org/toc/1029-8479Abstract We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one “electric” and the other “magnetic”. Each can be obtained from the corresponding Lorentz-invariant theory written in Hamiltonian form through the same “contraction” procedure of taking the ultrarelativistic limit c → 0 where c is the speed of light, but with two different consistent rescalings of the canonical variables. This procedure can be applied to general Lorentz-invariant theories (p-form gauge fields, higher spin free theories etc) and has the advantage of providing explicitly an action principle from which the electrically-contracted or magnetically-contracted dynamics follow (and not just the equations of motion). Even though not manifestly so, this Hamiltonian action principle is shown to be Carroll invariant. In the case of p-forms, we construct explicitly an equivalent manifestly Carroll-invariant action principle for each Carroll contraction. While the manifestly covariant variational description of the electric contraction is rather direct, the one for the magnetic contraction is more subtle and involves an additional pure gauge field, whose elimination modifies the Carroll transformations of the fields. We also treat gravity, which constitutes one of the main motivations of our study, and for which we provide the two different contractions in Hamiltonian form.Marc HenneauxPatricio Salgado-RebolledoSpringerOpenarticleSpace-Time SymmetriesField Theories in Higher DimensionsClassical Theories of GravityNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-29 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Space-Time Symmetries Field Theories in Higher Dimensions Classical Theories of Gravity Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Space-Time Symmetries Field Theories in Higher Dimensions Classical Theories of Gravity Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Marc Henneaux Patricio Salgado-Rebolledo Carroll contractions of Lorentz-invariant theories
description	Abstract We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one “electric” and the other “magnetic”. Each can be obtained from the corresponding Lorentz-invariant theory written in Hamiltonian form through the same “contraction” procedure of taking the ultrarelativistic limit c → 0 where c is the speed of light, but with two different consistent rescalings of the canonical variables. This procedure can be applied to general Lorentz-invariant theories (p-form gauge fields, higher spin free theories etc) and has the advantage of providing explicitly an action principle from which the electrically-contracted or magnetically-contracted dynamics follow (and not just the equations of motion). Even though not manifestly so, this Hamiltonian action principle is shown to be Carroll invariant. In the case of p-forms, we construct explicitly an equivalent manifestly Carroll-invariant action principle for each Carroll contraction. While the manifestly covariant variational description of the electric contraction is rather direct, the one for the magnetic contraction is more subtle and involves an additional pure gauge field, whose elimination modifies the Carroll transformations of the fields. We also treat gravity, which constitutes one of the main motivations of our study, and for which we provide the two different contractions in Hamiltonian form.
format	article
author	Marc Henneaux Patricio Salgado-Rebolledo
author_facet	Marc Henneaux Patricio Salgado-Rebolledo
author_sort	Marc Henneaux
title	Carroll contractions of Lorentz-invariant theories
title_short	Carroll contractions of Lorentz-invariant theories
title_full	Carroll contractions of Lorentz-invariant theories
title_fullStr	Carroll contractions of Lorentz-invariant theories
title_full_unstemmed	Carroll contractions of Lorentz-invariant theories
title_sort	carroll contractions of lorentz-invariant theories
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/e9ae0bf9a75946d695608bfe032d198d
work_keys_str_mv	AT marchenneaux carrollcontractionsoflorentzinvarianttheories AT patriciosalgadorebolledo carrollcontractionsoflorentzinvarianttheories
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Carroll contractions of Lorentz-invariant theories

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