Deterministic computation of functional integrals Original Research Article

A new method of numerical integration in functional spaces is described. This method is based on the rigorous definition of a functional integral in complete separable metric space and on the use of approximation formulas which we constructed for this kind of integral. No preliminary discretization of space and time is required in this method, as well as no simplifying assumptions like semiclassical approximation, collective excitations, introduction of “short-time” propagators, etc., are necessary in our approach. The comparison with results of other authors shows that our method gives significant economy of computer time and memory versus other known methods while providing the results with the same or better accuracy. The method is proved to have advantages also in a case of systems with many degrees of freedom. Examples of application of the method to the numerical study of some physical models are presented.