Some Identities for the Quantum Measure and its Generalizations

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.

(v1) 19 pages, LaTeX. (v2) 18 pages, LaTeX: minor corrections, simplified proof of lemma 3

References in corpus (1)

• Forks in the Road, on the Way to Quantum Gravity

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