194 research outputs found
Path integration in relativistic quantum mechanics
The simple physics of a free particle reveals important features of the
path-integral formulation of relativistic quantum theories. The exact
quantum-mechanical propagator is calculated here for a particle described by
the simple relativistic action proportional to its proper time. This propagator
is nonvanishing outside the light cone, implying that spacelike trajectories
must be included in the path integral. The propagator matches the WKB
approximation to the corresponding configuration-space path integral far from
the light cone; outside the light cone that approximation consists of the
contribution from a single spacelike geodesic. This propagator also has the
unusual property that its short-time limit does not coincide with the WKB
approximation, making the construction of a concrete skeletonized version of
the path integral more complicated than in nonrelativistic theory.Comment: 14 page
Law Learning, Teacher-Student Relations, and the Legal Profession
Innovation and change in legal education, extending the scope of the enterprise as it is now conducted, appear essential to strong moral, intellectual, and social purpose
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