Phase Space
The path integral considers the particle's trajectory in phase space, defined by its position and momentum, contributing to the overall amplitude.
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The statement of the theorem
The phase space is defined by the coordinates , where is the position and is the canonical momentum. The path integral formulation can be extended to include the evolution in phase space, often involving the Wigner function or the Moyal bracket, where the measure is . The propagator in phase space is related to the Wigner transform of the density matrix .