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arXiv:physics/9803035

The probability in the relativistic m+1 space-time

Gunn Quznetsov

Published Mar 25, 1998• 2 citations
arXivHTMLPDF

Abstract

The probability behavior in the m+1 relativistic space-time is considered. The probability, which is defined by the relativistic m+1-vector of the probability density, is investigated.
DOI
10.48550/arxiv.physics/9803035

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The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative 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 space–time 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.