Convolution of n-dimensional Tempered Ultradistributions and Field Theory

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 Ultra...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Bollini, Carlos Guido, Rocca, Mario Carlos
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2004
Materias:
Física
Quantum mechanics
Formalism
Functional analytical methods
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/131842
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-131842
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Quantum mechanics
Formalism
Functional analytical methods
spellingShingle Física
Quantum mechanics
Formalism
Functional analytical methods
Bollini, Carlos Guido
Rocca, Mario Carlos
Convolution of n-dimensional Tempered Ultradistributions and Field Theory
topic_facet Física
Quantum mechanics
Formalism
Functional analytical methods
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 $k^0$ and $\rho$ (see Section 5) we obtain an expression for the convolution, which is more suitable for practical applications. The product of two arbitrary even (in the variables $x^0$ 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 Wheeeler's propagators and the convolution of two complex mass Wheeler's propagators.
format Articulo
Preprint
author Bollini, Carlos Guido
Rocca, Mario Carlos
author_facet Bollini, Carlos Guido
Rocca, Mario Carlos
author_sort Bollini, Carlos Guido
title Convolution of n-dimensional Tempered Ultradistributions and Field Theory
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
publishDate 2004
url http://sedici.unlp.edu.ar/handle/10915/131842
work_keys_str_mv AT bollinicarlosguido convolutionofndimensionaltemperedultradistributionsandfieldtheory
AT roccamariocarlos convolutionofndimensionaltemperedultradistributionsandfieldtheory
bdutipo_str Repositorios
_version_ 1764820453459755008

Ejemplares similares