## Journal of Physical Mathematics

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

### Nonassociative quantum theory on octooctonion algebra

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 25 October 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.jpm/1288015153

**Digital Object Identifier**

doi:10.4303/jpm/S090501

**Zentralblatt MATH identifier**

1264.81248

**Subjects**

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

**Keywords**

Quantum theory octooctonion algebra

#### Citation

Köplinger, Jens. Nonassociative quantum theory on octooctonion algebra. J. Phys. Math. 1 (2009), Article ID S090501, 14 pages. doi:10.4303/jpm/S090501. https://projecteuclid.org/euclid.jpm/1288015153