2,190 research outputs found
Octonions and Super Lie algebra
We discuss how to represent the non-associative octonionic structure in terms
of the associative matrix algebra using the left and right octonionic
operators. As an example we construct explicitly some Lie and Super Lie
algebra. Then we discuss the notion of octonionic Grassmann numbers and explain
its possible application for giving a superspace formulation of the minimal
supersymmetric Yang-Mills models.Comment: RevTex file, 12 pages, to be published in Int. J. of Mod. Phys. A;
Some references adde
Octonionic Quantum Mechanics and Complex Geometry
The use of complex geometry allows us to obtain a consistent formulation of
octonionic quantum mechanics (OQM). In our octonionic formulation we solve the
hermiticity problem and define an appropriate momentum operator within OQM. The
nonextendability of the completeness relation and the norm conservation is also
discussed in details.Comment: To appear in Prog. Theor. Phys. (vol 96
- …