Geodesic
Quantum corrections to the effective potential in nonrenormalizable theories
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 3, pp. 533-542 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For the effective potential in the leading logarithmic approximation, we construct a renormalization group equation that holds for arbitrary scalar field theories, including nonrenormalizable ones, in four dimensions. This equation reduces to the usual renormalization group equation with a one-loop beta-function in the renormalizable case. The solution of this equation sums up the leading logarithmic contributions in the field in all orders of the perturbation theory. This is a nonlinear second-order partial differential equation in general, but it can be reduced to an ordinary one in some cases. In specific examples, we propose a numerical solution of this equation and construct the effective potential in the leading logarithmic approximation. We consider two examples as an illustration: a power-law potential and a cosmological potential of the $\operatorname{tan}^2\phi$ type. The obtained equation in physically interesting cases opens up the possibility of studying the properties of the effective potential, the presence of additional minima, spontaneous symmetry breaking, stability of the ground state, etc.
Keywords: scalar field theory, effective potential, nonrenormalizable theories, renormalization group. 
@article{TMF_2023_217_3_a6,
     author = {D. I. Kazakov and D. M. Tolkachev and R. M. Yahibbaev},
     title = {Quantum corrections to the~effective potential in nonrenormalizable theories},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {533--542},
     year = {2023},
     volume = {217},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_217_3_a6/}
}
TY  - JOUR
AU  - D. I. Kazakov
AU  - D. M. Tolkachev
AU  - R. M. Yahibbaev
TI  - Quantum corrections to the effective potential in nonrenormalizable theories
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 533
EP  - 542
VL  - 217
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_217_3_a6/
LA  - ru
ID  - TMF_2023_217_3_a6
ER  - 
%0 Journal Article
%A D. I. Kazakov
%A D. M. Tolkachev
%A R. M. Yahibbaev
%T Quantum corrections to the effective potential in nonrenormalizable theories
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 533-542
%V 217
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2023_217_3_a6/
%G ru
%F TMF_2023_217_3_a6
D. I. Kazakov; D. M. Tolkachev; R. M. Yahibbaev. Quantum corrections to the effective potential in nonrenormalizable theories. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 3, pp. 533-542. http://geodesic.mathdoc.fr/item/TMF_2023_217_3_a6/

[1] S. Coleman, E. Weinberg, “Radiative corrections as the origin of spontaneous symmetry breaking”, Phys. Rev. D, 7:6 (1973), 1888–1910 | DOI

[2] R. Jackiw, “Functional evaluation of the effective potential”, Phys. Rev. D, 9:6 (1974), 1686–1701 | DOI

[3] N. N. Bogoliubow, O. S. Parasiuk, “Über die multiplikation der Kausalfunktionen in der Quantentheorie der Felder”, Acta Math., 97 (1957), 227–266 | DOI | MR

[4] K. Hepp, “Proof of the Bogolyubov–Parasiuk theorem on renormalization”, Commun. Math. Phys., 2:1 (1966), 301–326 | DOI

[5] W. Zimmermann, “Convergence of Bogoliubov's method of renormalization in momentum space”, Commun. Math. Phys., 15:3 (1969), 208–234 | DOI | MR

[6] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1984 | MR | MR

[7] L. V. Bork, D. I. Kazakov, M. V. Kompaniets, D. M. Tolkachev, D. E. Vlasenko, “Divergences in maximal supersymmetric Yang–Mills theories in diverse dimensions”, JHEP, 11 (2015), 059, 38 pp. | DOI | MR

[8] D. I. Kazakov, L. V. Bork, A. T. Borlakov, D. M. Tolkachev, D. E. Vlasenko, “High energy behaviour in maximally supersymmetric gauge theories in various dimensions”, Symmetry, 11:1 (2019), 104, 29 pp. | DOI

[9] D. I. Kazakov, “RG equations and high energy behaviour in non-renormalizable theories”, Phys. Lett. B, 797 (2019), 134801, 5 pp. | DOI | MR

[10] R. Kallosh, A. Linde, “Universality class in conformal inflation”, J. Cosmol. Astropart. Phys., 2013:7 (2013), 002, arXiv: 1306.5220 | DOI

[11] Y. Akrami, R. Kallosh, A. Linde, V. Vardanyan, “Dark energy, $\alpha$-attractors, and large-scale structure surveys”, J. Cosmol. Astropart. Phys., 2018:6 (2018), 041, arXiv: 1712.09693 | DOI

[12] C. F. Curtiss, J. O. Hirschfelder, “Integration of stiff equations”, Proc. Natl. Acad. Sci. USA, 38:3 (1952), 235–243 | DOI