= Gaussian momentum integration in a phase-space path integral
{c}
{title2=$\int dp\,e^{-\Delta t p^2/(2m)+ip\Delta q}=\sqrt{2\pi m/\Delta t}\,e^{-m\Delta q^2/(2\Delta t)}$}
Integrating each momentum in a quadratic <Hamiltonian> yields the configuration-space kinetic action and its time-slice normalization. A raw $dp$ measure gives $\sqrt{2\pi m/\Delta t}$; the normalized Fourier measure $dp/(2\pi)$ gives $\sqrt{m/(2\pi\Delta t)}$. Dropping the time dependence changes the <quantum-mechanical propagator>.
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