Time-sliced configuration-space path integral

For a Hamiltonian operator with kinetic term ${\hat{p}}^2/2$, insert position-basis resolutions between Trotter product formula factors. The measure is the limit of $(2\pi i\Delta {)}^{-M/2}{\prod }_{j=1}^{M-1}d{q}_j$, and the exponent contains ${\sum }_j[(q_j-q_{j-1}{)}^2/(2\Delta )-\Delta V(q_{j-1})]$. Its continuum notation is $\int \mathcal{D}q{e}^{iS[q]}$, with fixed endpoint values. A damping prescription defines the oscillatory limit.