Time-sliced diffusion path integral
= Time-sliced diffusion path integral
For <diffusion> constant $D>0$, Gaussian increments have <variance> $2D\Delta t$. Their <convolution> gives a path weight proportional to $\exp[-\sum(\Delta x)^2/(4D\Delta t)]$ with measure factor $(4\pi D\Delta t)^{-M/2}$ for $M$ slices. The continuum kinetic <action> is notation for this limiting measure; typical Brownian paths have no ordinary derivative.