Geodesic
Nonperturbative vacuum energy density in two-dimensional scalar models
Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 1, pp. 72-86 
S. K. Karepanov. Nonperturbative vacuum energy density in two-dimensional scalar models. Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 1, pp. 72-86. http://geodesic.mathdoc.fr/item/TMF_1984_60_1_a7/
@article{TMF_1984_60_1_a7,
     author = {S. K. Karepanov},
     title = {Nonperturbative vacuum energy density in two-dimensional scalar models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {72--86},
     year = {1984},
     volume = {60},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_60_1_a7/}
}
TY  - JOUR
AU  - S. K. Karepanov
TI  - Nonperturbative vacuum energy density in two-dimensional scalar models
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1984
SP  - 72
EP  - 86
VL  - 60
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1984_60_1_a7/
LA  - ru
ID  - TMF_1984_60_1_a7
ER  - 
%0 Journal Article
%A S. K. Karepanov
%T Nonperturbative vacuum energy density in two-dimensional scalar models
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 72-86
%V 60
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1984_60_1_a7/
%G ru
%F TMF_1984_60_1_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

An upper bound that is uniform with respect to the coupling constant $g$ and the field is obtained for the effective potential for a two-dimensional scalar field theory with arbitrary self-interaction. The “nonexistence” of the :$\cos\alpha\varphi$: and :$\varphi^{2N}\exp\alpha\varphi$: models for $\alpha^2\geq 8\pi$ is proved. Exact asymptotic behaviors with respect to $g$ are found for the vacuum energy density for the $P(\varphi)_2$ and Hoegh-Krohn :$\exp\alpha\varphi$: models, and also for the total propagator at zero momentum.

[1] Efimov G. V., Commun. Math. Phys., 65:1 (1979), 15–44 | DOI | MR | Zbl

[2] Efimov G. V., Commun. Math. Phys., 57:5 (1977), 235–255 | DOI | MR

[3] Saimon B., Model $P(\varphi)_2$ evklidovoi kvantovoi teorii polya, Mir, M., 1976, 357 pp.

[4] Albeverio S., Hoegh-Krohn R., Quantum Fields - Algebras, Processes, ed. Streit L., Academic Press, N. Y., 1980, 331 pp. | MR

[5] Frolich J., Commun. Math. Phys., 47:5 (1976), 233–253 | DOI | MR

[6] Coleman S., Phys. Rev., D11:9 (1975), 2088–2098

[7] Carey A. L., Lohe M. A., O'Brien D. M., Commun. Math. Phys., 82:3 (1981), 191–210 | DOI | MR

[8] Mcshane E. J., Bull. Amer. Math. Soc., 69:3 (1963), 597–611 | DOI | MR

[9] Efimov G. V., Nelokalnye vzaimodeistviya kvantovannykh polei, Nauka, M., 1977, 366 pp. | MR

[10] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976, 542 pp. | MR