On Convergence of the Schwinger - DeWitt Expansion

Details On Convergence of the Schwinger - DeWitt Expansion On Convergence of the Schwinger - DeWitt Expansion

1997-10-17

arxiv.org/abs/hep-th/9710143v1

Mod.Phys.Lett. A12 (1997) 2889-2904

Physics

High Energy Physics

High Energy Physics - Theory

17 pp., LaTeX, to appear in "Modern Physics Letters A"

Scientific paper

10.1142/S0217732397003010

The Schwinger - DeWitt expansion for the evolution operator kernel of the Schrodinger equation is studied for convergence. It is established that divergence of this expansion which is usually implied for all continuous potentials, excluding ones of the form V(q)=aq^2+bq+c, really takes place only if the coupling constant g is treated as independent variable. But the expansion may be convergent for some kinds of the potentials and for some discrete values of the charge, if the latter is considered as fixed parameter. Class of such potentials is interesting because inside of it the property of discreteness of the charge in the nature is reproduced in the theory in natural way.

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