C. Castro: Nonass. Octonionic Ternary Gauge Field Th.

Nonassociative Octonionic Ternary Gauge Field Theories

by Carlos Castro
Center for Theoretical Studies of Physical Systems
Clark Atlanta University, Atlanta, Georgia. 30314, perelmanc_at_hotmail.com
November, 2010, submitted to: J. Phys. A : Math and Theor.

A novel (to our knowledge) nonassociative and noncommutative octonionic ternary gauge field theory is explicitly constructed that it is based on a ternary-bracket structure involving the octonion algebra. The ternary bracket was defined earlier by Yamazaki. The field strengths F_{mu nu} are given in terms of the 3-bracket [B_mu,B_nu, Phi] involving an auxiliary octonionic-valued scalar field Phi = Phi^a e_a which plays the role of a ”coupling” function. In the concluding remarks a list of relevant future investigations are briefly outlined.

Keywords: Octonions, ternary algebras, Lie 3-algebras, membranes, nonassociative gauge theories, nonassociative geometry.

Source: Email by C. Castro, 2010/11/27 19:09, czarlosromanov_at_yahoo.com


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