Abstract
Convergence of the Schwinger–DeWittexpansion for the evolution operator kernel for specialclass of potentials is studied. It is shown that thisexpansion, which is in the general case asymptotic,converges for the potentials considered (widely used, inparticular, in one-dimensional many-body problems), andthat convergence takes place only for definite discretevalues of the coupling constant. For other values of the charge, a divergent expansiondetermines the kernels having essential singularity atthe origin (beyond the usual δ-function). If oneconsiders only this class of potentials, then one can avoid many problems connected withasymptotic expansions, and one gets a theory withdiscrete values of the coupling constant that is incorrespondence with the discreteness of charge innature. This approach can be applied to quantum fieldtheory.
Similar content being viewed by others
REFERENCES
Barvinsky, A. O., Osborn, T. A., and Gusev, Yu. V. (1995). Journal of Mathematical Physics, 36, 30.
Bender, C. M., and Wu, T. T. (1969). Physical Review, 184, 1231.
Bender, C. M., and Wu, T. T. (1971a). Physical Review Letters, 27, 461.
Bender, C. M., and Wu, T. T. (1971b). Physical Review D 7, 1620.
Calogero, F., Marchioro, C., and Ragnisco, O. (1975). Lettere al Nuovo Cimento, 13, 383.
DeWitt, B. S. (1965). Dynamical Theory of Groups and Fields, Gordon and Breach, New York.
DeWitt, B. S. (1975). Physics Reports, 19, 297.
Halliday, I. G., and Suranyi P. (1980). Physical Review D 21, 1529.
Kazakov, D. I., and Shirkov, D. V. (1980). Fortschritte der Physik, 28, 465.
Lipatov, L. N. (1977). Zhurnal Experimentalnoy i Teoreticheskoy Fiziki, 72, 411.
Olshanetsky, A. O., and Perelomov, A. M. (1983). Physics Reports, 94, 315.
Osborn, T. A., and Fujiwara, Y. (1983). Journal of Mathematical Physics, 24, 1093.
Popov, V. S., Sergeev, A. V., and Shcheblykin, A. V. (1992). Zhurnal Experimentalno y i Teoreticheskoy Fiziki, 102, 1453.
Schwinger, J. (1951). Physical Review, 82, 664.
Sissakian, A. N., and Solovtsov, I. L. (1992). Zeitschrift für Physik C, 54, 263.
Slobodenyuk, V. A. (1993). Zeitschrift für Physik C, 58, 575.
Slobodenyuk, V. A. (1995). Theoretical and Mathematical Physics, 105, 1387 [hep-th/9412001 ].
Slobodenyuk, V. A. (1996a). Modern Physics Letters A, 11, 1729 [hep-th/9605188 ].
Slobodenyuk, V. A. (1996b). Theoretical and Mathematical Physics, 109, 1302.
Sutherland, B. (1971). Physical Review A, 4, 2019.
Sutherland, B. (1972). Physical Review A, 5, 1372.
Ushveridze, A. G. (1983). Yadernaya Fizika, 38, 798.
Rights and permissions
About this article
Cite this article
Slobodenyuk, V.A. Potentials with Convergent Schwinger–DeWitt Expansion. International Journal of Theoretical Physics 37, 1753–1771 (1998). https://doi.org/10.1023/A:1026648826455
Issue Date:
DOI: https://doi.org/10.1023/A:1026648826455