Convolution of Lorentz Invariant 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
A general definition of convolution between two arbitrary four-dimensional Lorentz invariant (fdLi) tempered ultradistributions is given, in both Minkowski and Euclidean space (spherically symmetric tempered Ultradistributions). The product of two arbitrary fdLi distributions of exponential type is defined via the convolution of its corresponding Fourier transforms. Several examples of convolution of two fdLi tempered ultadisrtibutions are given. In particular, we calculate exactly the convolution of two Feynman's massless prapagators. An expression for the Fourier transform of a Lorentz invariant tempered ultradistribution in terms of modified Bessel distributions is obtained in this work (generalization of Bochner's formula to Minkowski space). From the deduction of the convoltion formula, we obtain the generalization to the Minkowski space, of the dimensional regularization of the perturbation theory of Green functions in the Euclidean configuration space given in Erdelyi (Higher Transcendental Functions, 1953). As an example we evaluate the convolution of two n-dimensional complex-mass Wheeler propagators.
Fil: Bollini, C. G.. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina
Fil: Rocca, Mario Carlos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. 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:11336/72327

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network_name_str CONICET Digital (CONICET)
spelling Convolution of Lorentz Invariant Ultradistributions and Field TheoryBollini, C. G.Rocca, Mario CarlosFormalismFoundationsFunctional Analytical MethodsQuantum Field TheoryUltradistributionshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1A general definition of convolution between two arbitrary four-dimensional Lorentz invariant (fdLi) tempered ultradistributions is given, in both Minkowski and Euclidean space (spherically symmetric tempered Ultradistributions). The product of two arbitrary fdLi distributions of exponential type is defined via the convolution of its corresponding Fourier transforms. Several examples of convolution of two fdLi tempered ultadisrtibutions are given. In particular, we calculate exactly the convolution of two Feynman's massless prapagators. An expression for the Fourier transform of a Lorentz invariant tempered ultradistribution in terms of modified Bessel distributions is obtained in this work (generalization of Bochner's formula to Minkowski space). From the deduction of the convoltion formula, we obtain the generalization to the Minkowski space, of the dimensional regularization of the perturbation theory of Green functions in the Euclidean configuration space given in Erdelyi (Higher Transcendental Functions, 1953). As an example we evaluate the convolution of two n-dimensional complex-mass Wheeler propagators.Fil: Bollini, C. G.. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; ArgentinaFil: Rocca, Mario Carlos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. 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 Publishers2004-04info: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/11336/72327Bollini, C. G.; Rocca, Mario Carlos; Convolution of Lorentz Invariant Ultradistributions and Field Theory; Springer/Plenum Publishers; International Journal of Theoretical Physics; 43; 4; 4-2004; 1019-10510020-7748CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/hep-th/0312214info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1023/B:IJTP.0000048599.21501.93info:eu-repo/semantics/altIdentifier/doi/10.1023/B:IJTP.0000048599.21501.93info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:33:22Zoai:ri.conicet.gov.ar:11336/72327instacron: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 09:33:23.242CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Convolution of Lorentz Invariant Ultradistributions and Field Theory
title Convolution of Lorentz Invariant Ultradistributions and Field Theory
spellingShingle Convolution of Lorentz Invariant Ultradistributions and Field Theory
Bollini, C. G.
Formalism
Foundations
Functional Analytical Methods
Quantum Field Theory
Ultradistributions
title_short Convolution of Lorentz Invariant Ultradistributions and Field Theory
title_full Convolution of Lorentz Invariant Ultradistributions and Field Theory
title_fullStr Convolution of Lorentz Invariant Ultradistributions and Field Theory
title_full_unstemmed Convolution of Lorentz Invariant Ultradistributions and Field Theory
title_sort Convolution of Lorentz Invariant 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 A general definition of convolution between two arbitrary four-dimensional Lorentz invariant (fdLi) tempered ultradistributions is given, in both Minkowski and Euclidean space (spherically symmetric tempered Ultradistributions). The product of two arbitrary fdLi distributions of exponential type is defined via the convolution of its corresponding Fourier transforms. Several examples of convolution of two fdLi tempered ultadisrtibutions are given. In particular, we calculate exactly the convolution of two Feynman's massless prapagators. An expression for the Fourier transform of a Lorentz invariant tempered ultradistribution in terms of modified Bessel distributions is obtained in this work (generalization of Bochner's formula to Minkowski space). From the deduction of the convoltion formula, we obtain the generalization to the Minkowski space, of the dimensional regularization of the perturbation theory of Green functions in the Euclidean configuration space given in Erdelyi (Higher Transcendental Functions, 1953). As an example we evaluate the convolution of two n-dimensional complex-mass Wheeler propagators.
Fil: Bollini, C. G.. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina
Fil: Rocca, Mario Carlos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. 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 A general definition of convolution between two arbitrary four-dimensional Lorentz invariant (fdLi) tempered ultradistributions is given, in both Minkowski and Euclidean space (spherically symmetric tempered Ultradistributions). The product of two arbitrary fdLi distributions of exponential type is defined via the convolution of its corresponding Fourier transforms. Several examples of convolution of two fdLi tempered ultadisrtibutions are given. In particular, we calculate exactly the convolution of two Feynman's massless prapagators. An expression for the Fourier transform of a Lorentz invariant tempered ultradistribution in terms of modified Bessel distributions is obtained in this work (generalization of Bochner's formula to Minkowski space). From the deduction of the convoltion formula, we obtain the generalization to the Minkowski space, of the dimensional regularization of the perturbation theory of Green functions in the Euclidean configuration space given in Erdelyi (Higher Transcendental Functions, 1953). As an example we evaluate the convolution of two n-dimensional complex-mass Wheeler propagators.
publishDate 2004
dc.date.none.fl_str_mv 2004-04
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/11336/72327
Bollini, C. G.; Rocca, Mario Carlos; Convolution of Lorentz Invariant Ultradistributions and Field Theory; Springer/Plenum Publishers; International Journal of Theoretical Physics; 43; 4; 4-2004; 1019-1051
0020-7748
CONICET Digital
CONICET
url http://hdl.handle.net/11336/72327
identifier_str_mv Bollini, C. G.; Rocca, Mario Carlos; Convolution of Lorentz Invariant Ultradistributions and Field Theory; Springer/Plenum Publishers; International Journal of Theoretical Physics; 43; 4; 4-2004; 1019-1051
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/arxiv/https://arxiv.org/abs/hep-th/0312214
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1023/B:IJTP.0000048599.21501.93
info:eu-repo/semantics/altIdentifier/doi/10.1023/B:IJTP.0000048599.21501.93
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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