Nonlocal Fractional Quantum Field Theory and Converging Perturbation Series

Abstract

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 PT for the generating functional (GF) of complete Green functions (including disconnected parts of functions) $\mathcal{Z}\left[j\right]$ as well as for GF of connected Green functions $\mathcal{G}\left[j\right]=\ln \mathcal{Z}\left[j\right]$ 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 to expand beyond the weak coupling $g$ limit. Vacuum energy density in second order in $g$ is calculated and researched for different types of Gaussian part $S_0[\varphi ]$ of the action $S[\varphi ]$. Further in the paper, using the polynomial expansion, the general calculable series for $\mathcal{G}\left[j\right]$ 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 considering system across the entire range of coupling constant $g$, in particular, the vacuum energy density.

arXiv commentV1 - raw preprint; V2 - fix of language; V3 - significantly revised preprint, MDPI template

References in corpus (14)

• Fundamentals of the Exact Renormalization Group
• Super-renormalizable & Finite Gravitational Theories
• Coulomb systems at low density
• Ultraviolet Complete Quantum Gravity
• Nonlocal quantum gravity and M-theory
• Realization of symmetry in the ERG approach to quantum field theory
• Finite quantum gravity in dS and AdS spacetimes
• Ultraviolet Complete Electroweak Model Without a Higgs Particle
• Duality in Quantum Liouville Theory
• Abelian Anomalies in Nonlocal Regularization
• $\mathcal{S}$-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions
• Nonlocal Scalar Quantum Field Theory: Functional Integration, Basis Functions Representation and Strong Coupling Expansion
• On Functional Hamilton-Jacobi and Schrödinger Equations and Functional Renormalization Group
• A Note on Efimov Nonlocal and Nonpolynomial Quantum Scalar Field Theory

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