On Convergence of the Schwinger - DeWitt Expansion
High Energy Physics - Theory
2009-10-30 v1
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/9710143,
title = {On Convergence of the Schwinger - DeWitt Expansion},
author = {V. A. Slobodenyuk},
journal= {arXiv preprint arXiv:hep-th/9710143},
year = {2009}
}
Comments
17 pp., LaTeX, to appear in "Modern Physics Letters A"