Communications in Information and Systems

Volume 14 (2014)

Number 3

Split-complex numbers and Dirac bra-kets

Pages: 135 – 159



Steven Deckelman (Department of Mathematics, Statistics and Computer Science, University of Wisconsin-Stout, Menomonie, Wisc., U.S.A.)

Barry Robson (Quantal Semantics Inc., North Carolina, U.S.A.; St. Matthews University, Cayman Islands; and The Dirac Foundation, Oxfordshire, England)


We describe the real tessarines or “split-complex numbers” and describe a novel instance where they arise in biomedical informatics. We use the split-complex numbers to give a mathematical definition of a Hyperbolic Dirac Network (HDN)—a hyperbolic analogue of a classical probabilistic graphical model that uses quantum physics as an underlying heuristic.

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