Convolution of n-Dimensional Tempered Ultradistributions and Field Theory

Autores
Bollini, C. G.; Rocca, Mario Carlos
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work, a general definition of convolution between two arbitrary tempered ultradistributions is given. When one of the tempered ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva. In the four-dimensional case, when the tempered ultradistributions are even in the variables k0 and ρ, we obtain an expression for the convolution, which is more suitable for practical applications. The product of two arbitrary even (in the variables x0 and r) four-dimensional distributions of exponential type is defined via the convolution of its corresponding Fourier transforms. With this definition of convolution, we treat the problem of singular products of Green Functions in Quantum Field Theory (for Renormalizable as well as for nonrenormalizable theories). Several examples of convolution of two tempered ultradistributions are given. In particular, we calculate the convolution of two massless Wheeler's propagators and the convolution of two complex mass Wheeler's propagators.
Fil: Bollini, C. G.. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; 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
Materia
Formalism
Foundations
Functional Analytical Methods
Quantum Field Theory
Ultradistributions
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/72452
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/72452
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Convolution of n-Dimensional Tempered Ultradistributions and Field TheoryBollini, C. G.Rocca, Mario CarlosFormalismFoundationsFunctional Analytical MethodsQuantum Field TheoryUltradistributionshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In this work, a general definition of convolution between two arbitrary tempered ultradistributions is given. When one of the tempered ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva. In the four-dimensional case, when the tempered ultradistributions are even in the variables k0 and ρ, we obtain an expression for the convolution, which is more suitable for practical applications. The product of two arbitrary even (in the variables x0 and r) four-dimensional distributions of exponential type is defined via the convolution of its corresponding Fourier transforms. With this definition of convolution, we treat the problem of singular products of Green Functions in Quantum Field Theory (for Renormalizable as well as for nonrenormalizable theories). Several examples of convolution of two tempered ultradistributions are given. In particular, we calculate the convolution of two massless Wheeler's propagators and the convolution of two complex mass Wheeler's propagators.Fil: Bollini, C. G.. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; 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; ArgentinaSpringer/Plenum Publishers2004-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/72452Bollini, C. G.; Rocca, Mario Carlos; Convolution of n-Dimensional Tempered Ultradistributions and Field Theory; Springer/Plenum Publishers; International Journal of Theoretical Physics; 43; 1; 1-2004; 59-760020-7748CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1023/B:IJTP.0000028850.35090.24info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/hep-th/0309271info:eu-repo/semantics/altIdentifier/doi/10.1023/B:IJTP.0000028850.35090.24info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:46:47Zoai:ri.conicet.gov.ar:11336/72452instacron: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 09:46:47.457CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Convolution of n-Dimensional Tempered Ultradistributions and Field Theory
title Convolution of n-Dimensional Tempered Ultradistributions and Field Theory
spellingShingle Convolution of n-Dimensional Tempered Ultradistributions and Field Theory
Bollini, C. G.
Formalism
Foundations
Functional Analytical Methods
Quantum Field Theory
Ultradistributions
title_short Convolution of n-Dimensional Tempered Ultradistributions and Field Theory
title_full Convolution of n-Dimensional Tempered Ultradistributions and Field Theory
title_fullStr Convolution of n-Dimensional Tempered Ultradistributions and Field Theory
title_full_unstemmed Convolution of n-Dimensional Tempered Ultradistributions and Field Theory
title_sort Convolution of n-Dimensional Tempered Ultradistributions and Field Theory
dc.creator.none.fl_str_mv Bollini, C. G.
Rocca, Mario Carlos
author Bollini, C. G.
author_facet Bollini, C. G.
Rocca, Mario Carlos
author_role author
author2 Rocca, Mario Carlos
author2_role author
dc.subject.none.fl_str_mv Formalism
Foundations
Functional Analytical Methods
Quantum Field Theory
Ultradistributions
topic Formalism
Foundations
Functional Analytical Methods
Quantum Field Theory
Ultradistributions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work, a general definition of convolution between two arbitrary tempered ultradistributions is given. When one of the tempered ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva. In the four-dimensional case, when the tempered ultradistributions are even in the variables k0 and ρ, we obtain an expression for the convolution, which is more suitable for practical applications. The product of two arbitrary even (in the variables x0 and r) four-dimensional distributions of exponential type is defined via the convolution of its corresponding Fourier transforms. With this definition of convolution, we treat the problem of singular products of Green Functions in Quantum Field Theory (for Renormalizable as well as for nonrenormalizable theories). Several examples of convolution of two tempered ultradistributions are given. In particular, we calculate the convolution of two massless Wheeler's propagators and the convolution of two complex mass Wheeler's propagators.
Fil: Bollini, C. G.. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; 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
description In this work, a general definition of convolution between two arbitrary tempered ultradistributions is given. When one of the tempered ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva. In the four-dimensional case, when the tempered ultradistributions are even in the variables k0 and ρ, we obtain an expression for the convolution, which is more suitable for practical applications. The product of two arbitrary even (in the variables x0 and r) four-dimensional distributions of exponential type is defined via the convolution of its corresponding Fourier transforms. With this definition of convolution, we treat the problem of singular products of Green Functions in Quantum Field Theory (for Renormalizable as well as for nonrenormalizable theories). Several examples of convolution of two tempered ultradistributions are given. In particular, we calculate the convolution of two massless Wheeler's propagators and the convolution of two complex mass Wheeler's propagators.
publishDate 2004
dc.date.none.fl_str_mv 2004-01
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/11336/72452
Bollini, C. G.; Rocca, Mario Carlos; Convolution of n-Dimensional Tempered Ultradistributions and Field Theory; Springer/Plenum Publishers; International Journal of Theoretical Physics; 43; 1; 1-2004; 59-76
0020-7748
CONICET Digital
CONICET
url http://hdl.handle.net/11336/72452
identifier_str_mv Bollini, C. G.; Rocca, Mario Carlos; Convolution of n-Dimensional Tempered Ultradistributions and Field Theory; Springer/Plenum Publishers; International Journal of Theoretical Physics; 43; 1; 1-2004; 59-76
0020-7748
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://link.springer.com/article/10.1023/B:IJTP.0000028850.35090.24
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/hep-th/0309271
info:eu-repo/semantics/altIdentifier/doi/10.1023/B:IJTP.0000028850.35090.24
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer/Plenum Publishers
publisher.none.fl_str_mv Springer/Plenum Publishers
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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score 13.070432

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