A physical basis for the phase in Feynman path integration
  In the path integral formulation of quantum mechanics, the phase factor Exp[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 phase itself can have a physical origin in time reversal, and that the propagator can be drawn by a single deterministic path. 
G.N. Ord, J. A. Gualtieri, R.B. Mann