The 0D quantum field theory: Multiple integrals via background field formalism

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Abstract

A variant of ``0D quantum field theory'' alternative of random matrices is proposed. The Feynman's path integrals are directly replaced by usual multiple Riemannian ones over finite-dimensional real Euclidean space. In this scheme we realized L. D. Faddeev's version of background field formalism. As an example the $\varphi^4$ model is discussed. Necessary Feynman diagram technics is constructed. If diagrams in each order of the perturbation theory (or the loop expansion) are calculated, so, we have an asymptotic series for S-matrix generating functional. We suppose that the method will help calculate asymptotic expansions for special kind of integrals.
Original languageEnglish
Title of host publicationDays on Diffraction 2016
Subtitle of host publicationProceedings of the International Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages41-45
ISBN (Electronic)9781509058006
ISBN (Print)9781509058013
DOIs
StatePublished - 2016
Event2016 International Conference Days on Diffraction, DD 2016 - St. Petersburg, Russian Federation
Duration: 27 Jun 20161 Jul 2016

Conference

Conference2016 International Conference Days on Diffraction, DD 2016
CountryRussian Federation
CitySt. Petersburg
Period27/06/161/07/16

Keywords

  • background field formalism
  • $\phi^4$ model
  • diagram technics
  • asymptotic series

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