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100.1.#.a: Cabo Montes de Oca, Alejandro; González Lezcano, A.

524.#.#.a: Cabo Montes de Oca, Alejandro, et al. (2018). A relativistic formulation of the de la Peña-Cetto stochastic quantum mechanics. Revista Mexicana de Física; Vol 64, No 2 Mar-Apr: 158-171. Recuperado de https://repositorio.unam.mx/contenidos/4106900

245.1.0.a: A relativistic formulation of the de la Peña-Cetto stochastic quantum mechanics

502.#.#.c: Universidad Nacional Autónoma de México

561.1.#.a: Facultad de Ciencias, UNAM

264.#.0.c: 2018

264.#.1.c: 2018-03-14

653.#.#.a: Stochastic QED; Couder’s experiments

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001.#.#.#: oai:ojs.rmf.smf.mx:article/149

041.#.7.h: eng

520.3.#.a: A covariant generalization of a non-relativistic stochastic quantum mechanics introduced by de la Peña and Cetto is formulated. The analysis is done in space-time and avoids the use of a non-covariant time evolution parameter in order to search for Lorentz invariance. The covariant form of the set of iterative equations for the joint coordinate and momentum distribution function Q(x; p) is derived and expanded in power series of the coupling of the particle with the stochastic forces. Then, particular solutions of the zeroth order in the charge of the iterative equations for Q(x; p) are considered. For them, it follows that the space-time probability density ρ(x) and the function S(x) which gradient defines the mean value of the momentum at the space time point x, define a complex function ψ(x) which exactly satisfies the Klein-Gordon (KG) equation. These results for the zeroth order solution reproduce the ones formerly and independently derived in the literature. It is alsoargued that when the KG solution is either of positive or negative energy, the total number of particles conserves in the random motion. Other solutions for the joint distribution function in lowest order, satisfying the positive condition are also presented here. The are consistent with the assumed lack of stochastic forces implied by the zeroth order equations. It is also argued that such joint distributions, after considering the action of the stochastic forces, might furnish an explanation of the quantum mechanical properties, as associated to ensembles of particles in which the vacuum makes such particles behave in a similar way as Couder’s droplets moving over oscillating liquid surfaces. Some remarks on the solutions of the positive joint distribution problem proposed in the Olavos’s analysis are also presented.

773.1.#.t: Revista Mexicana de Física; Vol 64, No 2 Mar-Apr (2018): 158-171

773.1.#.o: https://rmf.smf.mx/ojs/rmf/index

046.#.#.j: 2020-11-25 00:00:00.000000

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doi: https://doi.org/10.31349/RevMexFis.64.158

handle: 008f8aa48902e5eb

harvesting_date: 2020-09-23 00:00:00.0

856.#.0.q: application/pdf

last_modified: 2020-11-27 00:00:00

license_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.es

license_type: by-nc-nd

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Artículo

A relativistic formulation of the de la Peña-Cetto stochastic quantum mechanics

Cabo Montes de Oca, Alejandro; González Lezcano, A.

Facultad de Ciencias, UNAM, publicado en Revista Mexicana de Física, y cosechado de Revistas UNAM

Licencia de uso

Procedencia del contenido

Entidad o dependencia
Facultad de Ciencias, UNAM
Revista
Repositorio
Contacto
Revistas UNAM. Dirección General de Publicaciones y Fomento Editorial, UNAM en revistas@unam.mx

Cita

Cabo Montes de Oca, Alejandro, et al. (2018). A relativistic formulation of the de la Peña-Cetto stochastic quantum mechanics. Revista Mexicana de Física; Vol 64, No 2 Mar-Apr: 158-171. Recuperado de https://repositorio.unam.mx/contenidos/4106900

Descripción del recurso

Autor(es)
Cabo Montes de Oca, Alejandro; González Lezcano, A.
Tipo
Artículo de Investigación
Área del conocimiento
Físico Matemáticas y Ciencias de la Tierra
Título
A relativistic formulation of the de la Peña-Cetto stochastic quantum mechanics
Fecha
2018-03-14
Resumen
A covariant generalization of a non-relativistic stochastic quantum mechanics introduced by de la Peña and Cetto is formulated. The analysis is done in space-time and avoids the use of a non-covariant time evolution parameter in order to search for Lorentz invariance. The covariant form of the set of iterative equations for the joint coordinate and momentum distribution function Q(x; p) is derived and expanded in power series of the coupling of the particle with the stochastic forces. Then, particular solutions of the zeroth order in the charge of the iterative equations for Q(x; p) are considered. For them, it follows that the space-time probability density ρ(x) and the function S(x) which gradient defines the mean value of the momentum at the space time point x, define a complex function ψ(x) which exactly satisfies the Klein-Gordon (KG) equation. These results for the zeroth order solution reproduce the ones formerly and independently derived in the literature. It is alsoargued that when the KG solution is either of positive or negative energy, the total number of particles conserves in the random motion. Other solutions for the joint distribution function in lowest order, satisfying the positive condition are also presented here. The are consistent with the assumed lack of stochastic forces implied by the zeroth order equations. It is also argued that such joint distributions, after considering the action of the stochastic forces, might furnish an explanation of the quantum mechanical properties, as associated to ensembles of particles in which the vacuum makes such particles behave in a similar way as Couder’s droplets moving over oscillating liquid surfaces. Some remarks on the solutions of the positive joint distribution problem proposed in the Olavos’s analysis are also presented.
Tema
Stochastic QED; Couder’s experiments
Idioma
eng
ISSN
2683-2224 (digital); 0035-001X (impresa)

Enlaces