Spacetime quantum and classical mechanics with dynamical foliation

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Díaz, Nahuel Luciano, Matera, Juan Mauricio, Rossignoli, Raúl Dante
Formato: Articulo
Lenguaje:Inglés
Publicado: 2024
Materias:
Física
Quantum Physics
Foundations of Quantum Mechanics
Quantum Field Theory
Covariant quantum mechanics
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/166574
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-166574
record_format dspace
spelling I19-R120-10915-1665742024-05-30T20:07:40Z http://sedici.unlp.edu.ar/handle/10915/166574 Spacetime quantum and classical mechanics with dynamical foliation Díaz, Nahuel Luciano Matera, Juan Mauricio Rossignoli, Raúl Dante 2024-05-06 2024-05-30T17:26:06Z en Física Quantum Physics Foundations of Quantum Mechanics Quantum Field Theory Covariant quantum mechanics 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 Articulo Articulo http://creativecommons.org/licenses/by-nc-nd/4.0/ Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) application/pdf
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Quantum Physics
Foundations of Quantum Mechanics
Quantum Field Theory
Covariant quantum mechanics
spellingShingle Física
Quantum Physics
Foundations of Quantum Mechanics
Quantum Field Theory
Covariant quantum mechanics
Díaz, Nahuel Luciano
Matera, Juan Mauricio
Rossignoli, Raúl Dante
Spacetime quantum and classical mechanics with dynamical foliation
topic_facet Física
Quantum Physics
Foundations of Quantum Mechanics
Quantum Field Theory
Covariant quantum mechanics
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.
format Articulo
Articulo
author Díaz, Nahuel Luciano
Matera, Juan Mauricio
Rossignoli, Raúl Dante
author_facet Díaz, Nahuel Luciano
Matera, Juan Mauricio
Rossignoli, Raúl Dante
author_sort Díaz, Nahuel Luciano
title Spacetime quantum and classical mechanics with dynamical foliation
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
publishDate 2024
url http://sedici.unlp.edu.ar/handle/10915/166574
work_keys_str_mv AT diaznahuelluciano spacetimequantumandclassicalmechanicswithdynamicalfoliation
AT materajuanmauricio spacetimequantumandclassicalmechanicswithdynamicalfoliation
AT rossignolirauldante spacetimequantumandclassicalmechanicswithdynamicalfoliation
_version_ 1807223278913191936

Ejemplares similares