Spacetime quantum and classical mechanics with dynamical foliation

Autores
Díaz, Nahuel Luciano; Matera, Juan Mauricio; Rossignoli, Raúl Dante
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions. First, we promote the time choice of the Legendre transform to a dynamical variable. Second, we extend the Poisson brackets of matter fields to a spacetime symmetric form. The ensuing “spacetime phase space” is employed to obtain an explicitly covariant version of Hamilton equations for relativistic field theories. A canonical-like quantization of the formalism is then presented in which the fields satisfy spacetime commutation relations and the foliation is quantum. In this approach, the classical action is also promoted to an operator and retains explicit covariance through its nonseparability in the matter-foliation partition. The problem of establishing a correspondence between the new noncausal framework (where fields at different times are independent) and conventional QM is solved through a generalization of spacelike correlators to spacetime. In this generalization, the Hamiltonian is replaced by the action, and conventional particles by off-shell particles. When the foliation is quantized, the previous map is recovered by conditioning on foliation eigenstates, in analogy with the Page and Wootters mechanism. We also provide an interpretation of the correspondence in which the causal structure of a given theory emerges from the quantum correlations between the system and an environment. This idea holds for general quantum systems and allows one to generalize the density matrix to an operator containing the information of correlators both in space and time.
Instituto de Física La Plata
Comisión de Investigaciones Científicas de la provincia de Buenos Aires
Materia
Física
Quantum Physics
Foundations of Quantum Mechanics
Quantum Field Theory
Covariant quantum mechanics
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-nd/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/166574

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network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Spacetime quantum and classical mechanics with dynamical foliationDíaz, Nahuel LucianoMatera, Juan MauricioRossignoli, Raúl DanteFísicaQuantum PhysicsFoundations of Quantum MechanicsQuantum Field TheoryCovariant quantum mechanicsThe conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions. First, we promote the time choice of the Legendre transform to a dynamical variable. Second, we extend the Poisson brackets of matter fields to a spacetime symmetric form. The ensuing “spacetime phase space” is employed to obtain an explicitly covariant version of Hamilton equations for relativistic field theories. A canonical-like quantization of the formalism is then presented in which the fields satisfy spacetime commutation relations and the foliation is quantum. In this approach, the classical action is also promoted to an operator and retains explicit covariance through its nonseparability in the matter-foliation partition. The problem of establishing a correspondence between the new noncausal framework (where fields at different times are independent) and conventional QM is solved through a generalization of spacelike correlators to spacetime. In this generalization, the Hamiltonian is replaced by the action, and conventional particles by off-shell particles. When the foliation is quantized, the previous map is recovered by conditioning on foliation eigenstates, in analogy with the Page and Wootters mechanism. We also provide an interpretation of the correspondence in which the causal structure of a given theory emerges from the quantum correlations between the system and an environment. This idea holds for general quantum systems and allows one to generalize the density matrix to an operator containing the information of correlators both in space and time.Instituto de Física La PlataComisión de Investigaciones Científicas de la provincia de Buenos Aires2024-05-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/166574enginfo:eu-repo/semantics/altIdentifier/issn/2470-0010info:eu-repo/semantics/altIdentifier/issn/2470-0029info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.109.105008info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T11:16:10Zoai:sedici.unlp.edu.ar:10915/166574Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 11:16:10.484SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Spacetime quantum and classical mechanics with dynamical foliation
title Spacetime quantum and classical mechanics with dynamical foliation
spellingShingle Spacetime quantum and classical mechanics with dynamical foliation
Díaz, Nahuel Luciano
Física
Quantum Physics
Foundations of Quantum Mechanics
Quantum Field Theory
Covariant quantum mechanics
title_short Spacetime quantum and classical mechanics with dynamical foliation
title_full Spacetime quantum and classical mechanics with dynamical foliation
title_fullStr Spacetime quantum and classical mechanics with dynamical foliation
title_full_unstemmed Spacetime quantum and classical mechanics with dynamical foliation
title_sort Spacetime quantum and classical mechanics with dynamical foliation
dc.creator.none.fl_str_mv Díaz, Nahuel Luciano
Matera, Juan Mauricio
Rossignoli, Raúl Dante
author Díaz, Nahuel Luciano
author_facet Díaz, Nahuel Luciano
Matera, Juan Mauricio
Rossignoli, Raúl Dante
author_role author
author2 Matera, Juan Mauricio
Rossignoli, Raúl Dante
author2_role author
author
dc.subject.none.fl_str_mv Física
Quantum Physics
Foundations of Quantum Mechanics
Quantum Field Theory
Covariant quantum mechanics
topic Física
Quantum Physics
Foundations of Quantum Mechanics
Quantum Field Theory
Covariant quantum mechanics
dc.description.none.fl_txt_mv The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions. First, we promote the time choice of the Legendre transform to a dynamical variable. Second, we extend the Poisson brackets of matter fields to a spacetime symmetric form. The ensuing “spacetime phase space” is employed to obtain an explicitly covariant version of Hamilton equations for relativistic field theories. A canonical-like quantization of the formalism is then presented in which the fields satisfy spacetime commutation relations and the foliation is quantum. In this approach, the classical action is also promoted to an operator and retains explicit covariance through its nonseparability in the matter-foliation partition. The problem of establishing a correspondence between the new noncausal framework (where fields at different times are independent) and conventional QM is solved through a generalization of spacelike correlators to spacetime. In this generalization, the Hamiltonian is replaced by the action, and conventional particles by off-shell particles. When the foliation is quantized, the previous map is recovered by conditioning on foliation eigenstates, in analogy with the Page and Wootters mechanism. We also provide an interpretation of the correspondence in which the causal structure of a given theory emerges from the quantum correlations between the system and an environment. This idea holds for general quantum systems and allows one to generalize the density matrix to an operator containing the information of correlators both in space and time.
Instituto de Física La Plata
Comisión de Investigaciones Científicas de la provincia de Buenos Aires
description The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions. First, we promote the time choice of the Legendre transform to a dynamical variable. Second, we extend the Poisson brackets of matter fields to a spacetime symmetric form. The ensuing “spacetime phase space” is employed to obtain an explicitly covariant version of Hamilton equations for relativistic field theories. A canonical-like quantization of the formalism is then presented in which the fields satisfy spacetime commutation relations and the foliation is quantum. In this approach, the classical action is also promoted to an operator and retains explicit covariance through its nonseparability in the matter-foliation partition. The problem of establishing a correspondence between the new noncausal framework (where fields at different times are independent) and conventional QM is solved through a generalization of spacelike correlators to spacetime. In this generalization, the Hamiltonian is replaced by the action, and conventional particles by off-shell particles. When the foliation is quantized, the previous map is recovered by conditioning on foliation eigenstates, in analogy with the Page and Wootters mechanism. We also provide an interpretation of the correspondence in which the causal structure of a given theory emerges from the quantum correlations between the system and an environment. This idea holds for general quantum systems and allows one to generalize the density matrix to an operator containing the information of correlators both in space and time.
publishDate 2024
dc.date.none.fl_str_mv 2024-05-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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dc.language.none.fl_str_mv eng
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info:eu-repo/semantics/altIdentifier/issn/2470-0029
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.109.105008
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
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instname:Universidad Nacional de La Plata
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reponame_str SEDICI (UNLP)
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instname_str Universidad Nacional de La Plata
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repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
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