This is a preview of subscription content, log in via an institution to check access.
Literature cited
R. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals [Russian translation], Mir, Moscow (1968).
R. P. Feynman, “Space-time approach to nonrelativistic quantum mechanics,” Rev. Mod. Phys.,20, 367–387 (1948).
M. Kac, “On some connections between probability theory and differential and integral equations,” Proc. 2nd Berkeley Symp. Math. Stat. Prob., University of California Press, Berkeley (1951), pp. 189–215.
K. Ito, “Wiener integral and Feynman integral,” Proc. 4th Berkeley Symp. Math. Stat. Prob., University of California Pres, Berkeley (1961), pp. 227–238.
K. Ito, “Generalized uniform complex measures in the Hilbertian metric space with their application to the Feynman path integral,” Proc. 5th Berkeley Symp. Math. Stat. Prob., University of California Press, Berkeley (1967), pp. 145–161.
V. P. Maslov and A. M. Chebotarev, “Jump discontinuous processes and their applications in quantum mechanics,” Itogi Nauki i Tekhniki (Probability Theory. Mathematical Statistics. Theoretical Cybernetics), Vol. 15 (197(), pp. 5–78.
Yu. L. Daletskii and S. V. Fomin, Measures and Differential Equations in InfiniteDimensional Spaces [in Russian], Nauka, Moscow (1983).
H. Watanabe, “Feynman-Kac formula associated with a system of partial differential operators,” J. Func. Anal.,65, No. 2, 203–235 (1986).
D. V. Ktitarev, “Feynman formula in phase space for a class of systems of pseudodifferential equations,” Mat. Zamatki,42, No. 1, 40–49 (1987).
T. Ichinose and H. Tamura, “Propagation of a Dirac particle. A path integral approach,” J. Math. Phys.,25, No. 7, 1810–1819 (1984).
T. Zastawniak, “Path integrals for the telegrapher's and Dirac equation: the analytic family of measures and the underlying Poisson process,” Bull. Pol. Acad. Sci. Math.,36, No. 5, 341–356 (1988).
D. Elseworthy and A. Truman, “Feynman maps, Cameron-Martin formulas and anharmonic oscillators,” Ann. Inst. Henri Poincaré,41, No. 2, 115–142 (1984).
O. G. Smolyanov and E. T. Shavgulidze, “Fourier transformation and pseudodifferential operators in superanalysis,” Dokl. Akad. Nauk SSSR,299, No. 4, 816–821 (1988).
O. G. Smolyanov and E. T. Shavgulidze, “Representation of the solutions of linear evolutionary second-order superdifferential equations by means of path integrals,” Dokl. Akad. Nauk SSSR,309, No. 3, 545–550 (1989).
A. Yu. Khrennikov, “Pseudodifferential equations in functional superanalysis. II. Feynman-Kac formula,” Differents. Urav.,25, No. 3, 505–514 (1989).
D. V. Ktitarev, “Functional integral and the Feynman-Kac formula in superspace,” Lett. Math. Phys.,18, 325–331 (1989).
A. Yu. Khrennikov, “Feynman measure in phase space and the symbols for infinite-dimensional pseudodifferential operators,” Mat. Zametki,37, No. 5, 734–742 (1985).
Author information
Authors and Affiliations
Additional information
Translated from Mathmaticheskie Zametki, Vol. 51, No. 5, pp. 44–50, May, 1992.
The authors wish to express their appreciation to O. G. Smolyanov, E. T. Shavgulidze, and A. Yu. Khrennikov for useful discussion.
Rights and permissions
About this article
Cite this article
Egikyan, R.S., Ktitarev, D.V. Feynman's formula in phase space for systems of pseudodifferential equations with analytic symbols. Math Notes 51, 453–457 (1992). https://doi.org/10.1007/BF01262176
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01262176