Stability properties of Feynman's operational calculus for exponential functions of noncommuting operators (Q1862265)

Feynman's operational calculus has been discussed by Johnson, Lapadus, Defacio, Jefferies and the author. In this paper, the author treats the stability properties of Feynman's operational calculus for exponential functions of noncommuting operators. He considers the stability of the distangled exponential function with respect to the time-ordering measures and the stability of the exponential distangling series with respect to the operator-valued functions. He also discusses the time-dependent perturbation theory of nonrelativistic quantum mechanics and application of the stability results to this perturbation theory.