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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 1996 Volume 109, Number 2, Pages 175–186 (Mi tmf1220)

This article is cited in 4 papers

On quantization of systems with actions unbounded from below

O. I. Zavialova, M. Kanenagab, A. I. Kirillova, V. Yu. Mamakina, M. Namikib, I. Ohbab, E. V. Polyachenkoa

a Independent University of Moscow
b Waseda University

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.

Received: 13.06.1996

DOI: 10.4213/tmf1220


 English version:
Theoretical and Mathematical Physics, 1996, 109:2, 1379–1387

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© Steklov Math. Inst. of RAS, 2024