Geodesic
Scaling violation and the appearance of mass in scalar quantum field theories
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 1, pp. 86-97
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In massless quantum field theories, scale invariance is violated in logarithmic dimensions. We discuss options for interpreting this effect as spontaneous mass emergence in the framework of skeleton self-consistency equations with the full propagator in the $\varphi^3$, $\varphi^4$, and $\varphi^6$ models of a scalar field $\varphi$.
Keywords: scaling violation, appearance of mass. 
@article{TMF_2023_217_1_a5,
     author = {A. L. Pismenskii and Yu. M. Pis'mak},
     title = {Scaling violation and the~appearance of mass in scalar quantum field theories},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {86--97},
     year = {2023},
     volume = {217},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_217_1_a5/}
}
TY  - JOUR
AU  - A. L. Pismenskii
AU  - Yu. M. Pis'mak
TI  - Scaling violation and the appearance of mass in scalar quantum field theories
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 86
EP  - 97
VL  - 217
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_217_1_a5/
LA  - ru
ID  - TMF_2023_217_1_a5
ER  - 
%0 Journal Article
%A A. L. Pismenskii
%A Yu. M. Pis'mak
%T Scaling violation and the appearance of mass in scalar quantum field theories
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 86-97
%V 217
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2023_217_1_a5/
%G ru
%F TMF_2023_217_1_a5
A. L. Pismenskii; Yu. M. Pis'mak. Scaling violation and the appearance of mass in scalar quantum field theories. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 1, pp. 86-97. http://geodesic.mathdoc.fr/item/TMF_2023_217_1_a5/

[1] K. G. Wilson, J. Kogut, “The renormalization group and the $\epsilon$-expansion”, Phys. Rep., 12:2 (1974), 75–199 | DOI

[2] A. N. Vasilev, Kvantovopolevaya renormgruppa v teorii kriticheskogo povedeniya i stokhasticheskoi dinamike, PIYaF, SPb., 1998 | DOI | MR | Zbl

[3] A. L. Pismensky, Yu. M. Pis'mak, “Scaling violation in massless scalar quantum field models in logarithmic dimensions”, J. Phys. A: Math. Theor., 48:32 (2015), 325401, 25 pp. | DOI | MR

[4] J. Kubo, M. Lindner, K. Schmitz, M. Yamada, “Planck mass and inflation as consequences of dynamically broken scale invariance”, Phys. Rev. D, 100:1 (2019), 015037, 17 pp., arXiv: 1811.05950 | DOI | MR

[5] E. M. Chudnovskii, “Spontannoe narushenie konformnoi invariantnosti i mekhanizm Khiggsa”, TMF, 35:3 (1978), 398–400 | DOI

[6] I. V. Kharuk, “Dinamicheskoe obrazovanie massy Planka i temnoi energii v affinnoi gravitatsii”, TMF, 209:1 (2021), 125–141, arXiv: 2002.12178 | DOI | DOI | MR

[7] G. Vitiello, Topological defects, fractals and the structure of quantum field theory, arXiv: 0807.2164

[8] C. De Dominicis, “Variational formulations of equilibrium statistical mechanics”, J. Math. Phys., 3:5 (1962), 983–1002 | DOI | MR

[9] C. De Dominicis, P. C. Martin, “Stationary entropy principle and renormalization in normal and superfluid systems. I. Algebraic formulation”, J. Math. Phys., 5:1 (1964), 14–30 | DOI | MR

[10] C. De Dominicis, P. C. Martin, “Stationary entropy principle and renormalization in normal and superfluid systems. II. Diagrammatic formulation”, J. Math. Phys., 5:1 (1964), 31–59 | DOI | MR

[11] Yu. M. Pismak, “Dokazatelstvo 3-neprivodimosti tretego preobrazovaniya Lezhandra”, TMF, 18:3 (1974), 299–309 | DOI | MR

[12] A. N. Vasilev, A. K. Kazanskii, Yu. M. Pismak, “Uravneniya dlya vysshikh preobrazovanii Lezhandra v terminakh 1-neprivodimykh vershin”, TMF, 19:2 (1974), 186–200 | DOI

[13] A. N. Vasilev, A. K. Kazanskii, Yu. M. Pismak, “Diagrammnyi analiz chetvertogo preobrazovaniya Lezhandra”, TMF, 20:2 (1974), 181–193 | DOI

[14] Yu. M. Pismak, “Kombinatornyi analiz problemy perekryvanii dlya vershin, starshikh chetyrekhkhvostki. I. Nekotorye topologicheskie svoistva grafikov Feinmana”, TMF, 24:1 (1975), 34–48 | DOI | MR | Zbl

[15] Yu. M. Pismak, “Kombinatornyi analiz problemy perekryvanii dlya vershin, starshikh chetyrekhkhvostki. II. Vysshie preobrazovaniya Lezhandra”, TMF, 24:2 (1975), 177–194 | DOI | MR | Zbl

[16] A. N. Vasilev, Yu. M. Pismak, Yu. R. Khonkonen, “Prostoi metod rascheta kriticheskikh indeksov v $1/n$-razlozhenii”, TMF, 46:2 (1981), 157–171 | DOI

[17] A. N. Vasilev, Yu. M. Pismak, Yu. R. Khonkonen, “$1/n$-Razlozhenie: raschet indeksov $\eta$ i $\nu$ v poryadke $1/n^2$ dlya proizvolnoi razmernosti”, TMF, 47:3 (1981), 291–306 | DOI

[18] A. N. Vasilev, Yu. M. Pismak, Yu. R. Khonkonen, “$1/n$-Razlozhenie: raschet indeksa $\eta$ v poryadke $1/n^3$ metodom konformnogo butstrapa”, TMF, 50:2 (1982), 195–206 | DOI

[19] Yu. M. Pis'mak, A. L. Pismensky, “Self-consistency equations for composite operators in models of quantum field theory”, Symmetry, 15:1 (2023), 132, 19 pp. | DOI

[20] V. A. Fok, Nachala kvantovoi mekhaniki, Nauka, M., 1976

[21] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, v. 3, Kvantovaya mekhanika (nerelyativistskaya teoriya), Nauka, M., 1989 | MR

[22] A. N. Vasilev, Funktsionalnye metody v kvantovoi teorii polya i statistike, Izd-vo Leningr. un-ta, L., 1976 | MR

[23] P. Ramon, Teoriya polya. Sovremennyi vvodnyi kurs, Mir, M., 1984 | MR | Zbl