Probability in relativistic quantum mechanics and foliation of spacetime

Details Probability in relativistic quantum mechanics and foliation of spacetime Probability in relativistic quantum mechanics and foliation of spacetime

2006-02-02

arxiv.org/abs/quant-ph/0602024v2

Int.J.Mod.Phys.A22:6243-6251,2007

Physics

Quantum Physics

9 pages, 3 figures, revised, new references, to appear in Int. J. Mod. Phys. A

Scientific paper

10.1142/S0217751X07038438

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be non-negative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of spacetime must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

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