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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/166574
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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 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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http://sedici.unlp.edu.ar/handle/10915/166574 |
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eng |
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eng |
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info:eu-repo/semantics/altIdentifier/issn/2470-0010 info:eu-repo/semantics/altIdentifier/issn/2470-0029 info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.109.105008 |
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