The Jacobi principal function in quantum mechanics
The canonical functional action in the path integral in phase space is discretized by linking each pair of consecutive vertebral points - qk and pk+1 or pk and qk+1 - through the invariant complete solution of the Hamilton-Jacobi equation associated with the classical path defined by these extremes....
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1999
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03054470_v32_n13_p2589_Ferraro http://hdl.handle.net/20.500.12110/paper_03054470_v32_n13_p2589_Ferraro |
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| Sumario: | The canonical functional action in the path integral in phase space is discretized by linking each pair of consecutive vertebral points - qk and pk+1 or pk and qk+1 - through the invariant complete solution of the Hamilton-Jacobi equation associated with the classical path defined by these extremes. When the measure is chosen to reflect the geometrical character of the propagator (it must behave as a density of weight 1/2 in both of its arguments), the resulting infinitesimal propagator is cast in the form of an expansion in a basis of short-time solutions of the wave equation, associated with the eigenfunctions of the initial momenta canonically conjugated to a set of normal coordinates. The operator ordering induced by this prescription is a combination of a symmetrization rule coming from the phase, and a derivative term coming from the measure. |
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