Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories

Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories

Recently it was found that quantum gravity theories may involve constructing a quantum theory on non-Cauchy hypersurfaces. However this is problematic since the ordinary Poisson brackets are not causal in this case. We suggest a method to identify classical brackets that are causal on 2+1 non-Cauchy...

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Main Authors: Merav Hadad, Levy Rosenblum
Format: Article
Language:English
Published: Elsevier 2020-02-01
Series:Physics Letters B
Online Access:http://www.sciencedirect.com/science/article/pii/S0370269319308664
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spelling doaj-6bbb97bbcaaa443496fea74d312ff7ca2020-11-25T01:31:16ZengElsevierPhysics Letters B0370-26932020-02-01801Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theoriesMerav Hadad0Levy Rosenblum1Corresponding author.; Department of Natural Sciences, The Open University of Israel, P.O.B. 808, Raanana 43107, IsraelDepartment of Natural Sciences, The Open University of Israel, P.O.B. 808, Raanana 43107, IsraelRecently it was found that quantum gravity theories may involve constructing a quantum theory on non-Cauchy hypersurfaces. However this is problematic since the ordinary Poisson brackets are not causal in this case. We suggest a method to identify classical brackets that are causal on 2+1 non-Cauchy hypersurfaces and use it in order to show that the evolution of scalars and vectors fields in the 3rd spatial direction can be constructed by using a Hamilton-like procedure. Finally, we discuss the relevance of this result to quantum gravity.http://www.sciencedirect.com/science/article/pii/S0370269319308664
collection DOAJ
language English
format Article
sources DOAJ
author Merav Hadad
Levy Rosenblum
spellingShingle Merav Hadad
Levy Rosenblum
Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories
Physics Letters B
author_facet Merav Hadad
Levy Rosenblum
author_sort Merav Hadad
title Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories
title_short Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories
title_full Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories
title_fullStr Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories
title_full_unstemmed Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories
title_sort derivation of hamilton-like equations on a non-cauchy hypersurface and their expected connection to quantum gravity theories
publisher Elsevier
series Physics Letters B
issn 0370-2693
publishDate 2020-02-01
description Recently it was found that quantum gravity theories may involve constructing a quantum theory on non-Cauchy hypersurfaces. However this is problematic since the ordinary Poisson brackets are not causal in this case. We suggest a method to identify classical brackets that are causal on 2+1 non-Cauchy hypersurfaces and use it in order to show that the evolution of scalars and vectors fields in the 3rd spatial direction can be constructed by using a Hamilton-like procedure. Finally, we discuss the relevance of this result to quantum gravity.
url http://www.sciencedirect.com/science/article/pii/S0370269319308664
work_keys_str_mv AT meravhadad derivationofhamiltonlikeequationsonanoncauchyhypersurfaceandtheirexpectedconnectiontoquantumgravitytheories
AT levyrosenblum derivationofhamiltonlikeequationsonanoncauchyhypersurfaceandtheirexpectedconnectiontoquantumgravitytheories
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