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Riccardo Rattazzi developed a path-integral account of quantum mechanics that connects interference, operator evolution and statistical methods. His notes derive the path integral from quantum time evolution, work out the free-particle propagator and treat Gaussian fluctuations.^[ref]

The weight $e^{iS/\hslash }$, with $S$ the action functional, is an amplitude with a phase, not a classical probability assigned to each path. Combining amplitudes before taking probabilities produces interference. Analytic continuation to Euclidean time then connects suitable quantum calculations with statistical-mechanical formulations, under the required convergence and boundary assumptions.