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 Zap. Nauchn. Sem. POMI, 2017, Volume 465, Pages 61–81 (Mi znsl6531)

Regularization of propagators with background field and their logarithms in $4$-dimensions

T. A. Bolokhov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We provide different attempts to regularize simultaneously background field dependent propagators and traces of their logarithms for quantum field models in $4$-dimensional euclidian space-time. As was shown in the literature, infinities in the trace of the logarithm and in higher order loop diagramms are of different nature and require different approaches in regularization. We argue that the trace of the loagarithm itself is a finite (w.r.t regularization parameter) quantity. While the correspondent divergence in the effective action arises from the measure of the functional integral imposed by some Ward-like identities.

Key words and phrases: background field method, functional integration, operator logarithm, Yang–Mills theory.

 Funding Agency Grant Number Russian Science Foundation 14-11-598

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Document Type: Article
UDC: 517.9

Citation: T. A. Bolokhov, “Regularization of propagators with background field and their logarithms in $4$-dimensions”, Questions of quantum field theory and statistical physics. Part 24, Zap. Nauchn. Sem. POMI, 465, POMI, St. Petersburg, 2017, 61–81

Citation in format AMSBIB
\Bibitem{Bol17} \by T.~A.~Bolokhov \paper Regularization of propagators with background field and their logarithms in $4$-dimensions \inbook Questions of quantum field theory and statistical physics. Part~24 \serial Zap. Nauchn. Sem. POMI \yr 2017 \vol 465 \pages 61--81 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6531}