Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature

Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature

We use the scalar field constructed in phase space to analyze the analogous Stefan-Boltzmann law and Casimir effect, both of them at finite temperature. The temperature is introduced by Thermo Field Dynamics (TFD) formalism and the quantities are analyzed once projected in the space of coordinates....

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Main Authors: R. G. G. Amorim, J. S. da Cruz Filho, A. F. Santos, S. C. Ulhoa
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in High Energy Physics
Online Access:http://dx.doi.org/10.1155/2018/1928280
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spelling doaj-bc73b783c4d84467bd69c87079f9149b2020-11-24T23:14:19ZengHindawi LimitedAdvances in High Energy Physics1687-73571687-73652018-01-01201810.1155/2018/19282801928280Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite TemperatureR. G. G. Amorim0J. S. da Cruz Filho1A. F. Santos2S. C. Ulhoa3Faculdade Gama, Universidade de Brasília, Setor Leste (Gama), 72444-240 Brasília, DF, BrazilInstituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Mato Grosso, BrazilInstituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Mato Grosso, BrazilInstituto de Física, Universidade de Brasília, 70910-900 Brasília, DF, BrazilWe use the scalar field constructed in phase space to analyze the analogous Stefan-Boltzmann law and Casimir effect, both of them at finite temperature. The temperature is introduced by Thermo Field Dynamics (TFD) formalism and the quantities are analyzed once projected in the space of coordinates. We show that using the framework of phase space it is possible to introduce a thermal energy which is related to temperature as it vanishes when the temperature tends to zero. In fact given such a correlation the formalism of TFD is equivalent when project is in momenta space when compared to coordinates space.http://dx.doi.org/10.1155/2018/1928280
collection DOAJ
language English
format Article
sources DOAJ
author R. G. G. Amorim
J. S. da Cruz Filho
A. F. Santos
S. C. Ulhoa
spellingShingle R. G. G. Amorim
J. S. da Cruz Filho
A. F. Santos
S. C. Ulhoa
Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature
Advances in High Energy Physics
author_facet R. G. G. Amorim
J. S. da Cruz Filho
A. F. Santos
S. C. Ulhoa
author_sort R. G. G. Amorim
title Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature
title_short Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature
title_full Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature
title_fullStr Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature
title_full_unstemmed Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature
title_sort stefan-boltzmann law and casimir effect for the scalar field in phase space at finite temperature
publisher Hindawi Limited
series Advances in High Energy Physics
issn 1687-7357
1687-7365
publishDate 2018-01-01
description We use the scalar field constructed in phase space to analyze the analogous Stefan-Boltzmann law and Casimir effect, both of them at finite temperature. The temperature is introduced by Thermo Field Dynamics (TFD) formalism and the quantities are analyzed once projected in the space of coordinates. We show that using the framework of phase space it is possible to introduce a thermal energy which is related to temperature as it vanishes when the temperature tends to zero. In fact given such a correlation the formalism of TFD is equivalent when project is in momenta space when compared to coordinates space.
url http://dx.doi.org/10.1155/2018/1928280
work_keys_str_mv AT rggamorim stefanboltzmannlawandcasimireffectforthescalarfieldinphasespaceatfinitetemperature
AT jsdacruzfilho stefanboltzmannlawandcasimireffectforthescalarfieldinphasespaceatfinitetemperature
AT afsantos stefanboltzmannlawandcasimireffectforthescalarfieldinphasespaceatfinitetemperature
AT sculhoa stefanboltzmannlawandcasimireffectforthescalarfieldinphasespaceatfinitetemperature
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