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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/72327
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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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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