Critical behavior and stability problem in a scalar field model
Main Article Content
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
Article Details
Copyright (c) 2022 Rochev V.

This work is licensed under a Creative Commons Attribution 4.0 International License.
Licensing and protecting the author rights is the central aim and core of the publishing business. Peertechz dedicates itself in making it easier for people to share and build upon the work of others while maintaining consistency with the rules of copyright. Peertechz licensing terms are formulated to facilitate reuse of the manuscripts published in journals to take maximum advantage of Open Access publication and for the purpose of disseminating knowledge.
We support 'libre' open access, which defines Open Access in true terms as free of charge online access along with usage rights. The usage rights are granted through the use of specific Creative Commons license.
Peertechz accomplice with- [CC BY 4.0]
Explanation
'CC' stands for Creative Commons license. 'BY' symbolizes that users have provided attribution to the creator that the published manuscripts can be used or shared. This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to the author.
Please take in notification that Creative Commons user licenses are non-revocable. We recommend authors to check if their funding body requires a specific license.
With this license, the authors are allowed that after publishing with Peertechz, they can share their research by posting a free draft copy of their article to any repository or website.
'CC BY' license observance:
License Name |
Permission to read and download |
Permission to display in a repository |
Permission to translate |
Commercial uses of manuscript |
CC BY 4.0 |
Yes |
Yes |
Yes |
Yes |
The authors please note that Creative Commons license is focused on making creative works available for discovery and reuse. Creative Commons licenses provide an alternative to standard copyrights, allowing authors to specify ways that their works can be used without having to grant permission for each individual request. Others who want to reserve all of their rights under copyright law should not use CC licenses.
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.