Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz Invariant Tempered Distributions

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...

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Autores principales: Plastino, Ángel Luis, Rocca, Mario Carlos
Formato: Articulo
Lenguaje:Inglés
Publicado: 2018
Materias:
Física
Dimensional regularization
Ultrahyperfunctions
Wheelerʼs propagators
Feynmanʼs propagators
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/125165
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-125165
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Dimensional regularization
Ultrahyperfunctions
Wheelerʼs propagators
Feynmanʼs propagators
spellingShingle Física
Dimensional regularization
Ultrahyperfunctions
Wheelerʼs propagators
Feynmanʼs propagators
Plastino, Ángel Luis
Rocca, Mario Carlos
Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz Invariant Tempered Distributions
topic_facet Física
Dimensional regularization
Ultrahyperfunctions
Wheelerʼs propagators
Feynmanʼs propagators
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).
format Articulo
Articulo
author Plastino, Ángel Luis
Rocca, Mario Carlos
author_facet Plastino, Ángel Luis
Rocca, Mario Carlos
author_sort Plastino, Ángel Luis
title Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz Invariant Tempered Distributions
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
publishDate 2018
url http://sedici.unlp.edu.ar/handle/10915/125165
work_keys_str_mv AT plastinoangelluis quantumfieldtheoryfeynmanwheelerpropagatorsdimensionalregularizationinconfigurationspaceandconvolutionoflorentzinvarianttempereddistributions
AT roccamariocarlos quantumfieldtheoryfeynmanwheelerpropagatorsdimensionalregularizationinconfigurationspaceandconvolutionoflorentzinvarianttempereddistributions
bdutipo_str Repositorios
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