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Carroll contractions of Lorentz-invariant theories

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...

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Autores principales: Henneaux, Marc, Salgado-Rebolledo, Patricio
Lenguaje:eng
Publicado: 2021
Materias:
Acceso en línea:http://cds.cern.ch/record/2781225
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author Henneaux, Marc
Salgado-Rebolledo, Patricio
author_facet Henneaux, Marc
Salgado-Rebolledo, Patricio
author_sort Henneaux, Marc
collection CERN
description 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 $c \rightarrow 0$ 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.
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spelling cern-27812252021-12-17T08:59:55Zhttp://cds.cern.ch/record/2781225engHenneaux, MarcSalgado-Rebolledo, PatricioCarroll contractions of Lorentz-invariant theoriesgr-qcGeneral Relativity and Cosmologyhep-thParticle Physics - TheoryWe 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 $c \rightarrow 0$ 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.arXiv:2109.06708oai:cds.cern.ch:27812252021-09-14
spellingShingle gr-qc
General Relativity and Cosmology
hep-th
Particle Physics - Theory
Henneaux, Marc
Salgado-Rebolledo, Patricio
Carroll contractions of Lorentz-invariant theories
title 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_short Carroll contractions of Lorentz-invariant theories
title_sort carroll contractions of lorentz-invariant theories
topic gr-qc
General Relativity and Cosmology
hep-th
Particle Physics - Theory
url http://cds.cern.ch/record/2781225
work_keys_str_mv AT henneauxmarc carrollcontractionsoflorentzinvarianttheories
AT salgadorebolledopatricio carrollcontractionsoflorentzinvarianttheories