Abstract:
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.
Citation:
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”, TMF, 109:2 (1996), 175–186; Theoret. and Math. Phys., 109:2 (1996), 1379–1387
\Bibitem{ZavKanKir96}
\by O.~I.~Zavialov, M.~Kanenaga, A.~I.~Kirillov, V.~Yu.~Mamakin, M.~Namiki, I.~Ohba, E.~V.~Polyachenko
\paper On quantization of systems with actions unbounded from below
\jour TMF
\yr 1996
\vol 109
\issue 2
\pages 175--186
\mathnet{http://mi.mathnet.ru/tmf1220}
\crossref{https://doi.org/10.4213/tmf1220}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1472467}
\zmath{https://zbmath.org/?q=an:0962.81522}
\transl
\jour Theoret. and Math. Phys.
\yr 1996
\vol 109
\issue 2
\pages 1379--1387
\crossref{https://doi.org/10.1007/BF02072004}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1996XM63500002}
Linking options:
https://www.mathnet.ru/eng/tmf1220
https://doi.org/10.4213/tmf1220
https://www.mathnet.ru/eng/tmf/v109/i2/p175
This publication is cited in the following 4 articles:
A. I. Kirillov, V. Yu. Mamakin, “Stochastic model of phase transition and metastability”, Theoret. and Math. Phys., 123:1 (2000), 494–503
A. I. Kirillov, “Stochastic quantization using a kerneled Langevin equation”, Theoret. and Math. Phys., 115:1 (1998), 410–417
Kirillov, AI, “On the theory of metastable states”, Foundations of Physics, 27:12 (1997), 1701
Lev I. Deych, V. A. Ignatchenko, A. A. Lisyansky, “Energy oscillations of scattered waves for disorder-induced crossing resonance”, Phys. Rev. B, 55:17 (1997), 11287