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December 2009 Nonassociative quantum theory on octooctonion algebra
Jens Köplinger
J. Phys. Math. 1: 1-14 (December 2009). DOI: 10.4303/jpm/S090501


Using octooctonions (i.e., octonions with octonion coefficients O×O), this paper expresses select findings from nonassociative quantum theory in harmonized notation: Nonrelativistic and relativistic spin operators, Pauli and Dirac matrices, Dirac equation with electromagnetic and gravitational field, and dimensional reduction from quaternionic spin. A generalization of the dimensional reduction program is proposed to argue that octooctonion algebra is wide enough to model a speculated quantum theory that contains all symmetries of the Standard Model, together with four-dimensional Euclidean quantum gravity. The most narrow candidate for such a formulation consists of four generalized Dirac matrices and a four-dimensional operator space with associated fields and charges. Algebraic properties of this relation will be discussed, together with a landscape choice between all possible octooctonionic relations of similar kind.


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Jens Köplinger. "Nonassociative quantum theory on octooctonion algebra." J. Phys. Math. 1 1 - 14, December 2009.


Published: December 2009
First available in Project Euclid: 25 October 2010

zbMATH: 1264.81248
Digital Object Identifier: 10.4303/jpm/S090501

Primary: 81R15

Keywords: octooctonion algebra , quantum theory

Rights: Copyright © 2009 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)


Vol.1 • December 2009
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