Dirac and Maxwell systems in split octonions

Abstract

The known equivalence of 8-dimensional chiral spinors and vectors, also referred to as triality, is discussed for (4+4)-space. Split octonionic representation of SO(4,4) and Spin(4,4) groups and the trilinear invariant form are explicitly written and compared with Clifford algebraic matrix representation. It is noted that the complete algebra of split octonionic basis units can be recovered from the Moufang and Malcev relations for the three vector-like elements. Lagrangians on split octonionic fields that generalize Dirac and Maxwell systems are constructed using group invariant forms. It is shown that corresponding equations are related to split octonionic analyticity conditions.

published version, 19 pages, no figures

References in corpus (8)

• Generalized Split-Octonion Electrodynamics
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• An octonionic formulation of the M-theory algebra
• Geometrical Applications of Split Octonions
• Rotations in the Space of Split Octonions
• Cosmological constant, supersymmetry, nonassociativity, and Big Numbers
• Geometry of the Non-Compact G(2)
• Algebraical Entropy and Arrow of Time