标题： 关于施温格-德维特展开式的收敛性 显示英文标题

标题： On Convergence of the Schwinger - DeWitt Expansion

摘要： 对于薛定谔方程的演化算子核的施温格-德维特展开式的收敛性进行了研究。已确定，通常认为对于所有连续势能，除了形式为V(q)=aq^2+bq+c的势能外，该展开式发散，实际上只有当耦合常数g被视为独立变量时才会发生发散。但如果电荷被视为固定参数，那么对于某些类型的势能和某些离散的电荷值，该展开式可能是收敛的。这类势能具有重要意义，因为在其内部，自然界中电荷的离散性在理论中以自然的方式被再现。 显示英文摘要

摘要： 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.