Generalization via Ultrahyperfunctions of a Gupta-Feynman Based Quantum Field Theory of Einstein’s Gravity

Ultrahyperfunctions (UHF) are the generalization and extension to the complex plane of Schwartz’ tempered distributions. This effort is an application to Einstein’s gravity (EG) of the mathematical theory of convolution of Ultrahyperfunctions developed by Bollini et al. [1] [2] [3] [4]. A simplified...

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Autores principales: Plastino, Ángel Luis, Rocca, Mario Carlos
Formato: Articulo
Lenguaje:Inglés
Publicado: 2020
Materias:
Física
Quantum field theory
Einstein gravity
Non-renormalizable theories
Unitarity
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/119307
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-119307
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 field theory
Einstein gravity
Non-renormalizable theories
Unitarity
spellingShingle Física
Quantum field theory
Einstein gravity
Non-renormalizable theories
Unitarity
Plastino, Ángel Luis
Rocca, Mario Carlos
Generalization via Ultrahyperfunctions of a Gupta-Feynman Based Quantum Field Theory of Einstein’s Gravity
topic_facet Física
Quantum field theory
Einstein gravity
Non-renormalizable theories
Unitarity
description Ultrahyperfunctions (UHF) are the generalization and extension to the complex plane of Schwartz’ tempered distributions. This effort is an application to Einstein’s gravity (EG) of the mathematical theory of convolution of Ultrahyperfunctions developed by Bollini et al. [1] [2] [3] [4]. A simplified version of these results was given in [5] and, based on them; a Quantum Field Theory (QFT) of EG [6] was obtained. Any kind of infinities is avoided by recourse to UHF. We will quantize EG by appealing to the most general quantization approach, the Schwinger-Feynman variational principle, which is more appropriate and rigorous that the popular functional integral method (FIM). FIM is not applicable here because our Lagrangian contains derivative couplings. We follow works by Suraj N. Gupta and Richard P. Feynman so as to undertake the construction of an EG-QFT. We explicitly use the Einstein Lagrangian as elaborated by Gupta [7], but choose a new constraint for the ensuing theory. In this way, we avoid the problem of lack of unitarity for the S matrix that afflicts the procedures of Gupta and Feynman. Simultaneously, we significantly simplify the handling of constraints, which eliminates the need to appeal to ghosts for guarantying unitarity of the theory. Our approach is obviously non-renormalizable. However, this inconvenience can be overcome by appealing to the mathematical theory developed by Bollini et al. [1] [2] [3] [4] [5]. Such developments were founded in the works of Alexander Grothendieck [8] and in the theory of Ultradistributions of Jose Sebastiao e Silva [9] (also known as Ultrahyperfunctions). Based on these works, an edifice has been constructed along two decades that are able to quantize non-renormalizable Field Theories (FT). Here we specialize this mathematical theory to discuss EG-QFT. Because we are using a Gupta-Feynman inspired EG Lagrangian, we are able to evade the intricacies of Yang-Mills theories.
format Articulo
Articulo
author Plastino, Ángel Luis
Rocca, Mario Carlos
author_facet Plastino, Ángel Luis
Rocca, Mario Carlos
author_sort Plastino, Ángel Luis
title Generalization via Ultrahyperfunctions of a Gupta-Feynman Based Quantum Field Theory of Einstein’s Gravity
title_short Generalization via Ultrahyperfunctions of a Gupta-Feynman Based Quantum Field Theory of Einstein’s Gravity
title_full Generalization via Ultrahyperfunctions of a Gupta-Feynman Based Quantum Field Theory of Einstein’s Gravity
title_fullStr Generalization via Ultrahyperfunctions of a Gupta-Feynman Based Quantum Field Theory of Einstein’s Gravity
title_full_unstemmed Generalization via Ultrahyperfunctions of a Gupta-Feynman Based Quantum Field Theory of Einstein’s Gravity
title_sort generalization via ultrahyperfunctions of a gupta-feynman based quantum field theory of einstein’s gravity
publishDate 2020
url http://sedici.unlp.edu.ar/handle/10915/119307
work_keys_str_mv AT plastinoangelluis generalizationviaultrahyperfunctionsofaguptafeynmanbasedquantumfieldtheoryofeinsteinsgravity
AT roccamariocarlos generalizationviaultrahyperfunctionsofaguptafeynmanbasedquantumfieldtheoryofeinsteinsgravity
bdutipo_str Repositorios
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