TOWARD A NEW TIME-DEPENDENT PATH INTEGRAL FORMALISM BASED ON RESTRICTED QUANTUM PROPAGATORS FOR PHYSICALLY REALIZABLE SYSTEMS

Various mathematical properties of the exact free and full short-real-time propagators in the coordinate representation are discussed. The viewpoint is emphasized that these properties, which prevent the use of the exact path integral formalism as a basis for straightforward computations and result in bizarre behavior wholly at odds with our (macroscopically conditioned) intuition, are never relevant, in connection with any experimentally realizable system. These computationally disasterous mathematical properties of the kinetic energy part of the propagator may be removed by means of restricting the wave packets which will be propagated to L2 functions which can be fitted, sufficiently accurately, by a polynomial of a specific degree within the envelope of the fitting function. This is an example of "prefiltering" oscillations whose frequency increases without bound (i.e., as the distance \x'- x\ travelled in short time tau). The decay in the kinetic energy, which characterizes any physically realizable system, has been achieved using our continuum distributed approximating functions, which limit the class of wave packets which can be propagated. We also discuss the role of the potential energy. Again, difficulties arise which could be addressed by potential energy cutoff procedures. However, the more desireable possibility of developing a smoothly prefiltered full propagator is pointed out.