Geodesic
Nonperturbative vacuum energy density in two-dimensional scalar models
Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 1, pp. 72-86

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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. 
@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},
     publisher = {mathdoc},
     volume = {60},
     number = {1},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_60_1_a7/}
}
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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/