= Time-sliced equivalence of phase-space and configuration-space path integrals
For $H=p^2/(2m)+V(q)$, time slices of length $\delta$ use $N$ <momentum> measures $dp_j/(2\pi\hbar)$ and $N-1$ intermediate coordinate measures. Each <momentum> <Gaussian integral> gives $[m/(2\pi i\hbar\delta)]^{1/2}\exp[im(q_j-q_{j-1})^2/(2\hbar\delta)]$. The resulting configuration integral has normalization $[m/(2\pi i\hbar\delta)]^{N/2}$. A common endpoint convention for $V$ and the <Trotter product formula> identify both limits with the same operator transition kernel; a damping or imaginary-time prescription defines the oscillatory integrals.
// Target: perturbative-quantum-field-theory.bigb
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