A Discrete, Deterministic Construction of the Phase in Feynman Paths

In the path-integral formulation of quantum mechanics, the phase factor e ^iS(x〈t〉) is associated with every path x〈t〉. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the complex phase was a mathematical device invoked to extract wave behaviour in a particle framework. In this paper we show that the continuous phase itself can have a discrete origin in time reversal and that the propagator can be drawn by a single deterministic path. ¹On leave from Department of Mathematics, Ryerson University, Toronto, Ontario Canada.