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 (inMinkowskian 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 Bolliniet al. Using the Inverse Fourier Transform we get the ring with zero divisors S'LA, defined as S'L = 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 BGfor 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 masslessWheeler’s propagators in Minkowskian space. The results obtained in this work have already allowed us to calculate the classical partitionfunction 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).
Instituto de Física La Plata
Materia
Física
Dimensional regularization
Ultrahyperfunctions
Wheelerʼs propagators
Feynmanʼs propagators
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/125165

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spelling Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz Invariant Tempered DistributionsPlastino, Ángel LuisRocca, Mario CarlosFísicaDimensional regularizationUltrahyperfunctionsWheelerʼs propagatorsFeynmanʼs propagatorsThe Dimensional Regularization (DR) of Bollini and Giambiagi(BG) can not be defined for all Schwartz Tempered Distributions Explicitly Lorentz Invariant(STDELI) S'<sub>L</sub>. 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 (inMinkowskian 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 Bolliniet al. Using the Inverse Fourier Transform we get the ring with zero divisors S'<sub>LA</sub>, defined as S'<sub>L</sub> = F⁻¹ {S'<sub>L</sub>} , where F⁻¹ denotes the Inverse Fourier Transform. In this manner we effect a dimensional regularization in momentum space (the ring S'<sub>L</sub>) via convolution, and a product of distributions in the corresponding configuration space (the ring S'<sub>LA</sub>). This generalizes the results obtained by BGfor 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 masslessWheeler’s propagators in Minkowskian space. The results obtained in this work have already allowed us to calculate the classical partitionfunction 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).Instituto de Física La Plata2018info: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/10915/125165enginfo:eu-repo/semantics/altIdentifier/issn/2399-6528info:eu-repo/semantics/altIdentifier/doi/10.1088/2399-6528/aaf186info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:29:53Zoai:sedici.unlp.edu.ar:10915/125165Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:29:53.465SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Física
Dimensional regularization
Ultrahyperfunctions
Wheelerʼs propagators
Feynmanʼs 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 Física
Dimensional regularization
Ultrahyperfunctions
Wheelerʼs propagators
Feynmanʼs propagators
topic Física
Dimensional regularization
Ultrahyperfunctions
Wheelerʼs propagators
Feynmanʼs propagators
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'<sub>L</sub>. 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 (inMinkowskian 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 Bolliniet al. Using the Inverse Fourier Transform we get the ring with zero divisors S'<sub>LA</sub>, defined as S'<sub>L</sub> = F⁻¹ {S'<sub>L</sub>} , where F⁻¹ denotes the Inverse Fourier Transform. In this manner we effect a dimensional regularization in momentum space (the ring S'<sub>L</sub>) via convolution, and a product of distributions in the corresponding configuration space (the ring S'<sub>LA</sub>). This generalizes the results obtained by BGfor 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 masslessWheeler’s propagators in Minkowskian space. The results obtained in this work have already allowed us to calculate the classical partitionfunction 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).
Instituto de Física La Plata
description The Dimensional Regularization (DR) of Bollini and Giambiagi(BG) can not be defined for all Schwartz Tempered Distributions Explicitly Lorentz Invariant(STDELI) S'<sub>L</sub>. 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 (inMinkowskian 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 Bolliniet al. Using the Inverse Fourier Transform we get the ring with zero divisors S'<sub>LA</sub>, defined as S'<sub>L</sub> = F⁻¹ {S'<sub>L</sub>} , where F⁻¹ denotes the Inverse Fourier Transform. In this manner we effect a dimensional regularization in momentum space (the ring S'<sub>L</sub>) via convolution, and a product of distributions in the corresponding configuration space (the ring S'<sub>LA</sub>). This generalizes the results obtained by BGfor 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 masslessWheeler’s propagators in Minkowskian space. The results obtained in this work have already allowed us to calculate the classical partitionfunction 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
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/125165
url http://sedici.unlp.edu.ar/handle/10915/125165
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/2399-6528
info:eu-repo/semantics/altIdentifier/doi/10.1088/2399-6528/aaf186
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
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repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
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