Journal of Physical Mathematics

Nonassociative quantum theory on octooctonion algebra

Jens Köplinger

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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.

Article information

J. Phys. Math., Volume 1 (2009), Article ID S090501, 14 pages.

First available in Project Euclid: 25 October 2010

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Zentralblatt MATH identifier

Primary: 81R15: Operator algebra methods [See also 46Lxx, 81T05]

Quantum theory octooctonion algebra


Köplinger, Jens. Nonassociative quantum theory on octooctonion algebra. J. Phys. Math. 1 (2009), Article ID S090501, 14 pages. doi:10.4303/jpm/S090501.

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