Critical behavior and stability problem in a scalar field model

Article Sidebar

Annals of Mathematics and Physics volume5-issue2 articles
PDF HTML
Submitted: November 15, 2022
Published: Nov 29, 2022
DOI: 10.17352/amp.000061

Main Article Content

Vladimir Rochev*
Division of Theoretical Physics, AA Logunov Institute for High Energy Physics, NRC Kurchatov Institute, 142281 Protvino, Russia

Abstract

As shown in the works [1-3], the asymptotic behavior of the propagator in the Euclidean region of momenta for the model of a complex scalar field φ and a real scalar field χ with the interaction gϕ*ϕχ drastically changes depending on the value of the coupling constant. For small values of the coupling, the propagator of the field φ behaves asymptotically as free, while in the strong-coupling region the propagator in the deep Euclidean region tends to be a constant.
In this paper, the influence of the vacuum stability problem of this model on this critical behavior is investigated. It is shown that within the framework of the approximations used, the addition of a stabilizing term of type ϕ4 to the Lagrangian leads to a renormalization of the mass and does not change the main effect of changing the ultraviolet behavior of the propagator.
PACS number: 11.10.Jj.

Downloads

Download data is not yet available.

Article Details

Rochev, V. (2022). Critical behavior and stability problem in a scalar field model. Annals of Mathematics and Physics, 5(2), 161–170. https://doi.org/10.17352/amp.000061
Mini Reviews

Copyright (c) 2022 Rochev V.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rochev VE. Asymptotic behavior and critical coupling in scalar Yukawa model. Int.J.Mod.Phys.Conf.Ser. 2018; 47: 1860095.

Rochev VE. On the phase structure of the vector-matrix scalar model in four dimensions. Eur.Phys.J. 2018; C78: 927.

Rochev VE. Asymptotic behavior in quantum-field models from Schwinger-Dyson equations, In: Asymptotic Behavior: An Overview. Ed.: Steve P. Riley. 2020; 53-100, Nova Science Publishers, New York.

Abreu LM, Malbouisson APC, Malbouisson JMC, Nery ES, Rodrigues SR. Thermodynamic behavior of the generalized scalar Yukawa model in a magnetic background. Nucl.Phys. 2014; B881: 327-342.

Chabysheva SS, Hiller JR. Nonperturbative light-front effective potential for static sources in quenched scalar Yukawa theory. Phys.Rev. 2022; D 1055: 056027.

Baym G. Inconsistency of Cubic Boson-Boson Interactions. Phys.Rev. 1960; 117: 886-888.

Gross F, Savkli C, Tjon J. The stability of the scalar χ2ϕ interaction. Phys.Rev. 2001;D64: 076008.

De Dominicis S, Martin PC. Stationary Entropy Principle and Renormalization in Normal and Superfluid Systems. I. Algebraic Formulation J. Math. Phys. 1964; 5:14-30

Dahmen HD, Jona-Lasinio G. Variational formulation of quantum field theory. Nuovo Cim. 1967; A52: 807-836.

Kazanskii AK, Vasilev AN. Legendre transformations for generating functionals in quantum field theory. Teor.Mat.Fiz. 1972; 12: 352-369.

Cornwall JM, Jackiw R, Tomboulis E. Effective Action for Composite Operators. Phys. Rev. 1974; D10: 2428-2440.

Blaizot JP, Pawlowski JM, Reinosa U. Functional renormalization group and 2PI effective action formalism. Annals of Physics. 2021; 431: 168549

Greiner W, Müller B, Rafelski J. Quantum Electrodynamics of Strong Fields (Springer, Berlin). 1985.

Gross F. Relativistic Quantum Mechanics and Field Theory (Wiley NY). 1999.

RiversRJ. Path Integral Methods in Quantum Field Theory (Cambridge Univ. Press). 1987.