arXiv:gr-qc/9903015 · Modern Physics Letters A

SOME IDENTITIES FOR THE QUANTUM MEASURE AND ITS GENERALIZATIONS

Roberto B. Salgado

Published Apr 20, 2002• 33 citations

Abstract

After a brief review of classical probability theory (measure theory), we present an observation (due to Sorkin) concerning an aspect of probability in quantum mechanics. Following Sorkin, we introduce a generalized measure theory based on a hierarchy of "sum-rules". The first sum-rule yields classical probability theory, and the second yields a generalized probability theory that includes quantum mechanics as a special case. We present some algebraic relations involving these sum-rules. This may be useful for the study of the higher-order sum-rules and possible generalizations of quantum mechanics. We conclude with some open questions and suggestions for further work.

DOI: 10.1142/s0217732302007041

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