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On quantization of systems with actions unbounded from below
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 2, pp. 175-186 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider two possible approaches to the problem of quantization of systems with actions unbounded from below. The first uses the Borel summation method applied to the perturbation expansion in coupling constant. The second is based on the kerneled Langevin equation of stochastic quantization. We show that in a simple model the first method gives some Schwinger functions even in the case where the standard path integrals diverge. The solutions of the kerneled Langevin equation for the model are studied in detail both analytically and numerically. The fictitious time averages are shown to have the limits which can be considered as the Schwinger functions. An evidence is presented that both methods may give the same results. 
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     author = {O. I. Zavialov and M. Kanenaga and A. I. Kirillov and V. Yu. Mamakin and M. Namiki and I. Ohba and E. V. Polyachenko},
     title = {On quantization of systems with actions unbounded from below},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {175--186},
     year = {1996},
     volume = {109},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_109_2_a1/}
}
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O. I. Zavialov; M. Kanenaga; A. I. Kirillov; V. Yu. Mamakin; M. Namiki; I. Ohba; E. V. Polyachenko. On quantization of systems with actions unbounded from below. Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 2, pp. 175-186. http://geodesic.mathdoc.fr/item/TMF_1996_109_2_a1/

[1] S. Graffi, V. Grecchi, B. Simon, Phys. Lett., 32B (1970), 631–634 | DOI | MR

[2] J.-P. Eckmann, J. Magnen, R. Seneor, Commun. Math. Phys., 39 (1975), 251–271 | DOI | MR

[3] J. Avron, I. Herbst, B. Simon, Schrödinger Operators with Magnetic Fields, Preprint, Princeton Univ., 1977 | MR

[4] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, Nauka, M., 1973 | MR

[5] R. Z. Khasminskii, Ustoichivost sistem differentsialnykh uravnenii pri sluchainom vozmuschenii ikh parametrov, Nauka, M., 1969

[6] M. Namiki, Stochastic Quantization, Springer, 1992 | MR

[7] J. D. Breit, S. Gupta, A. Zaks, Nucl. Phys., B 233 (1984), 61 | DOI

[8] S. Tanaka, M. Namiki, I. Ohba, M. Mizutani, N. Komoike, M. Kanenaga, Phys. Lett., B288 (1992), 129 | DOI

[9] M. Kanenaga, M. Mizutani, M. Namiki, I. Ohba, S. Tanaka, Prog. Theor. Phys., 91 (1994), 599–610 | DOI