Path integral solution by sum over perturbation series

A method for calculating the relativistic path integral solution via sum ov er perturbation series is given. As an application the exact path integral solution of the relativistic Aharonov-Bohm-Coulomb system is obtained by th e method. Different from the earlier treatment based on the space-time tran sformation and infinite multiple-valued trasformation of Kustaanheimo-Stief el in order to perform path integral, the method developed in this contribu tion involves only the explicit form of a simple Green's function and an ex plicit path integral is avoided. (C) 2000 American Institute of Physics. [S 0022-2488(00)05305-6].