A Note on Efimov Nonlocal and Nonpolynomial Quantum Scalar Field Theory

Guskov, V.A.; Иванов, М. Г.; Ogarkov, S. L.

doi:10.1134/s1063779621030059

Cited by 1 publication

(1 citation statement)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another complicated but interesting mathematical problem is the rigorous definition of the Dyson-Schwinger, Schwinger-Tomonaga and functional (nonperturbative, exact) renormalization group flow (FRG flow for short) equations in nonlocal QFT [42,44,45,[48][49][50][51][52][53]. These equations are formulated in terms of variational derivatives, therefore, they are differential.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Fractional Quantum Field Theory and Converging Perturbation Series

Ignatyuk,

Ogarkov,

Skliannyi

2023

Symmetry

View full text Add to dashboard Cite

The main purpose of this paper is to derive a new perturbation theory (PT) that has converging series. Such series arise in the nonlocal scalar quantum field theory (QFT) with fractional power potential. We construct a PT for the generating functional (GF) of complete Green functions (including disconnected parts of functions) Zj as well as for the GF of connected Green functions Gj=lnZj in powers of coupling constant g. It has infrared (IR)-finite terms. We prove that the obtained series, which has the form of a grand canonical partition function (GCPF), is dominated by a convergent series—in other words, has majorant, which allows for expansion beyond the weak coupling g limit. Vacuum energy density in second order in g is calculated and researched for different types of Gaussian part S0[ϕ] of the action S[ϕ]. Further in the paper, using the polynomial expansion, the general calculable series for Gj is derived. We provide, compare and research simplifications in cases of second-degree polynomial and hard-sphere gas (HSG) approximations. The developed formalism allows us to research the physical properties of the considered system across the entire range of coupling constant g, in particular, the vacuum energy density.

show abstract