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.
Cite
@article{arxiv.gr-qc/9903015,
title = {Some Identities for the Quantum Measure and its Generalizations},
author = {Roberto B. Salgado},
journal= {arXiv preprint arXiv:gr-qc/9903015},
year = {2009}
}
Comments
(v1) 19 pages, LaTeX. (v2) 18 pages, LaTeX: minor corrections, simplified proof of lemma 3