Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions

Autores
Plastino, Ángel Luis; Rocca, Mario Carlos
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Dimensional Regularization (DR) of Bollini and Giambiagi (BG) can not be defined for all Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S'L. In this paper we overcome such limitation and show that it can be generalized to all aforementioned STDELI and obtain a product in a ring with zero divisors. For this purpose, we resort to a formula obtained by Bollini and Rocca and demonstrate the existence of the convolution (in Minkowskian space) of such distributions. This is done by following a procedure similar to that used so as to define a general convolution between the Ultradistributions of J Sebastiao e Silva (JSS), also known as Ultrahyperfunctions, obtained by Bollini et al. Using the Inverse Fourier Transform we get the ring with zero divisors S'LA, defined as S'LA = F-1 {S'L}, where F-1 denotes the Inverse Fourier Transform. In this manner we effect a dimensional regularization in momentum space (the ring S'L) via convolution, and a product of distributions in the corresponding configuration space (the ring S'LA). This generalizes the results obtained by BG for Euclidean space. We provide several examples of the application of our new results in Quantum Field Theory (QFT). In particular, the convolution of n massless Feynman’s propagators and the convolution of n massless Wheeler’s propagators in Minkowskian space. The results obtained in this work have already allowed us to calculate the classical partition function of Newtonian gravity, for the first time ever, in the Gibbs’ formulation and in the Tsallis’ one. It is our hope that this convolution will allow one to quantize non-renormalizable Quantum Field Theories (QFT’s).
Fil: Plastino, Ángel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Rocca, Mario Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
DIMENSIONAL REGULARIZATION
FEYNMANʼS PROPAGATORS
ULTRAHYPERFUNCTIONS
WHEELERʼS PROPAGATORS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/100805

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network_name_str CONICET Digital (CONICET)
spelling Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributionsPlastino, Ángel LuisRocca, Mario CarlosDIMENSIONAL REGULARIZATIONFEYNMANʼS PROPAGATORSULTRAHYPERFUNCTIONSWHEELERʼS PROPAGATORShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The Dimensional Regularization (DR) of Bollini and Giambiagi (BG) can not be defined for all Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S'L. In this paper we overcome such limitation and show that it can be generalized to all aforementioned STDELI and obtain a product in a ring with zero divisors. For this purpose, we resort to a formula obtained by Bollini and Rocca and demonstrate the existence of the convolution (in Minkowskian space) of such distributions. This is done by following a procedure similar to that used so as to define a general convolution between the Ultradistributions of J Sebastiao e Silva (JSS), also known as Ultrahyperfunctions, obtained by Bollini et al. Using the Inverse Fourier Transform we get the ring with zero divisors S'LA, defined as S'LA = F-1 {S'L}, where F-1 denotes the Inverse Fourier Transform. In this manner we effect a dimensional regularization in momentum space (the ring S'L) via convolution, and a product of distributions in the corresponding configuration space (the ring S'LA). This generalizes the results obtained by BG for Euclidean space. We provide several examples of the application of our new results in Quantum Field Theory (QFT). In particular, the convolution of n massless Feynman’s propagators and the convolution of n massless Wheeler’s propagators in Minkowskian space. The results obtained in this work have already allowed us to calculate the classical partition function of Newtonian gravity, for the first time ever, in the Gibbs’ formulation and in the Tsallis’ one. It is our hope that this convolution will allow one to quantize non-renormalizable Quantum Field Theories (QFT’s).Fil: Plastino, Ángel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Rocca, Mario Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaIOP Publishing2018-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/100805Plastino, Ángel Luis; Rocca, Mario Carlos; Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions; IOP Publishing; Journal of Physics Communications; 2; 11; 11-2018; 115029-1150392399-6528CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/2399-6528/aaf186info:eu-repo/semantics/altIdentifier/doi/10.1088/2399-6528/aaf186info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:01:32Zoai:ri.conicet.gov.ar:11336/100805instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:01:33.243CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions
title Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions
spellingShingle Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions
Plastino, Ángel Luis
DIMENSIONAL REGULARIZATION
FEYNMANʼS PROPAGATORS
ULTRAHYPERFUNCTIONS
WHEELERʼS PROPAGATORS
title_short Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions
title_full Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions
title_fullStr Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions
title_full_unstemmed Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions
title_sort Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions
dc.creator.none.fl_str_mv Plastino, Ángel Luis
Rocca, Mario Carlos
author Plastino, Ángel Luis
author_facet Plastino, Ángel Luis
Rocca, Mario Carlos
author_role author
author2 Rocca, Mario Carlos
author2_role author
dc.subject.none.fl_str_mv DIMENSIONAL REGULARIZATION
FEYNMANʼS PROPAGATORS
ULTRAHYPERFUNCTIONS
WHEELERʼS PROPAGATORS
topic DIMENSIONAL REGULARIZATION
FEYNMANʼS PROPAGATORS
ULTRAHYPERFUNCTIONS
WHEELERʼS PROPAGATORS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The Dimensional Regularization (DR) of Bollini and Giambiagi (BG) can not be defined for all Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S'L. In this paper we overcome such limitation and show that it can be generalized to all aforementioned STDELI and obtain a product in a ring with zero divisors. For this purpose, we resort to a formula obtained by Bollini and Rocca and demonstrate the existence of the convolution (in Minkowskian space) of such distributions. This is done by following a procedure similar to that used so as to define a general convolution between the Ultradistributions of J Sebastiao e Silva (JSS), also known as Ultrahyperfunctions, obtained by Bollini et al. Using the Inverse Fourier Transform we get the ring with zero divisors S'LA, defined as S'LA = F-1 {S'L}, where F-1 denotes the Inverse Fourier Transform. In this manner we effect a dimensional regularization in momentum space (the ring S'L) via convolution, and a product of distributions in the corresponding configuration space (the ring S'LA). This generalizes the results obtained by BG for Euclidean space. We provide several examples of the application of our new results in Quantum Field Theory (QFT). In particular, the convolution of n massless Feynman’s propagators and the convolution of n massless Wheeler’s propagators in Minkowskian space. The results obtained in this work have already allowed us to calculate the classical partition function of Newtonian gravity, for the first time ever, in the Gibbs’ formulation and in the Tsallis’ one. It is our hope that this convolution will allow one to quantize non-renormalizable Quantum Field Theories (QFT’s).
Fil: Plastino, Ángel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Rocca, Mario Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description The Dimensional Regularization (DR) of Bollini and Giambiagi (BG) can not be defined for all Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S'L. In this paper we overcome such limitation and show that it can be generalized to all aforementioned STDELI and obtain a product in a ring with zero divisors. For this purpose, we resort to a formula obtained by Bollini and Rocca and demonstrate the existence of the convolution (in Minkowskian space) of such distributions. This is done by following a procedure similar to that used so as to define a general convolution between the Ultradistributions of J Sebastiao e Silva (JSS), also known as Ultrahyperfunctions, obtained by Bollini et al. Using the Inverse Fourier Transform we get the ring with zero divisors S'LA, defined as S'LA = F-1 {S'L}, where F-1 denotes the Inverse Fourier Transform. In this manner we effect a dimensional regularization in momentum space (the ring S'L) via convolution, and a product of distributions in the corresponding configuration space (the ring S'LA). This generalizes the results obtained by BG for Euclidean space. We provide several examples of the application of our new results in Quantum Field Theory (QFT). In particular, the convolution of n massless Feynman’s propagators and the convolution of n massless Wheeler’s propagators in Minkowskian space. The results obtained in this work have already allowed us to calculate the classical partition function of Newtonian gravity, for the first time ever, in the Gibbs’ formulation and in the Tsallis’ one. It is our hope that this convolution will allow one to quantize non-renormalizable Quantum Field Theories (QFT’s).
publishDate 2018
dc.date.none.fl_str_mv 2018-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/100805
Plastino, Ángel Luis; Rocca, Mario Carlos; Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions; IOP Publishing; Journal of Physics Communications; 2; 11; 11-2018; 115029-115039
2399-6528
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100805
identifier_str_mv Plastino, Ángel Luis; Rocca, Mario Carlos; Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions; IOP Publishing; Journal of Physics Communications; 2; 11; 11-2018; 115029-115039
2399-6528
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/2399-6528/aaf186
info:eu-repo/semantics/altIdentifier/doi/10.1088/2399-6528/aaf186
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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