= Path integral
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A <path integral> represents quantum evolution or <correlation functions> as an integral over histories. Dividing time into short steps, inserting resolutions of the identity and multiplying short-time kernels gives the familiar oscillatory weight $e^{iS/\hbar}$, together with a measure and boundary data.
The weight is a complex amplitude, not an ordinary <probability> assigned independently to each classical trajectory. Histories interfere, and stationary-phase configurations reproduce classical equations when the approximation is controlled. A <Euclidean path integral> uses <imaginary time> and a decaying <action> weight under suitable convergence conditions, helping study tunnelling and thermal states. A formal continuum expression must retain a definition of its discretization, operator ordering and normalization where they affect the result.
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