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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/125165
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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 |
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dc.language.none.fl_str_mv |
eng |
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