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

摘要

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 Φ4 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.