Semiclassical Propagation and the Dynamics of Configuration Space

This work explores the non-relativistic quantum propagator $K(x,t)$ as a solution of the Schr\"odinger equation. We suppose that the propagator takes the form ${\rm exp}\left(\frac{\mathrm{i}}{\hbar}S+R\right)$, generalizing the usual WKB ansatz by allowing an additive exponent $R$ whose role as a measure of quantumness is investigated. Since $S$ is subject to the assumption that it is a solution of the Hamilton-Jacobi equation, here we are further interested in the role of $R$ and its interpretation as a measure of quantumness. Several systems are studied as concrete examples to illustrate this approach. Furthermore, a proposal to generalize it for fields is put forward. This is tested for some simple systems. Finally, the possibilities to use this approach for the case of systems whose dynamics are controlled by the Hamiltonian constraint are analyzed.