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arXiv · gr-qc/9903015

Some Identities for the Quantum Measure and its Generalizations

Roberto B. Salgado
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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.

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Roberto B. Salgado. 2002-06-14. Some Identities for the Quantum Measure and its Generalizations. https://doi.org/10.1142/s0217732302007041

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