Time slicing of a phase-space path integral
= Time slicing of a phase-space path integral
{title2=$\dot q_i=(q_{i+1}-q_i)/\Delta t_i$}
The first-order term means $\sum_i p_i(q_{i+1}-q_i)$ in a finite-dimensional integral. Specify the endpoints and an ordering prescription, then take the maximum time step to zero. Typical Euclidean paths are not classically differentiable, so the discrete prescription is essential.