Classical dynamical origin of Feynman paths?
M. Roncadelli
Even though only the classical action explicitly appears in the Feynman path integral, quantum fluctuations show up in the fluctuating nature of Feynman paths. This prevents a classical interpretation of the latter objects. Still, it makes sense to ask whether the Feynman paths have any relation to the classical dynamical trajectories in configuration space-a possibility naturally suggested by the semiclassical approximation. Unfortunately, no such relation exists (in general). Things are quite different for the generalized Feynman paths, which actually contribute in a novel path integral giving an alternative representation of the quantum mechanical propagator. It is shown that these paths fluctuate about a classical dynamical trajectory (in configuration space) because of a certain white noise. That is to say, the generalized Feynman paths are fluctuating curves that collapse on a classical dynamical trajectory as h to 0. This result throws new light on the interplay between classical and quantum mechanics and hints at a new approach to the quantum theory.
Journal of Physics A Mathematical and General•Sep 21, 1993•3 citations