WHAT DOES OPERATOR ORDERING HAVE TO DO WITH THE DENSITY OF PATHS?

In joint work with M. Roncadelli, I have shown that the quantum Hamilton-Jacobi equation, which at one time attracted considerable attention but was abandoned as intractable, could be solved through its relation to the propagator. (Of course solving for the propagator is also far from trivial.) This article reviews that work and discusses applications. In one application we find that quantum operator ordering reveals the classical density of paths.