## On Octonionic Nonassociative Ternary Gauge Field Theories

**Authors:** Carlos Castro

A novel (to our knowledge) nonassociative Octonionic ternary gauge
field theory is explicitly constructed based on a ternary-bracket structure
involving the octonion algebra. The ternary bracket was defined earlier
by Yamazaki. The antisymmetric rank-two field strength F_{μν} is defined in
terms of the ternary-bracket (... see paper) involving an auxiliary octonionicvalued
coupling (...) . The ternary bracket cannot be rewritten
in terms of 2-brackets, [A,B,C] ≠ 1/4[[A,B],C]. It is found that gaugeinvariant
matter kinetic terms for an octonionic-valued scalar field can be
introduced in the action if one starts instead with an octonionic-valued
rank-three antisymmetric field strength (...)
permutations, which is defined in terms of an antisymmetric tensor field
of rank two (...) and (...) We conclude with some
preliminary steps towards the construction of generalized ternary gauge
field theories involving both 3-Lie algebras and octonions.

**Comments:** 11 pages, submitted to Physics Letters B

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### Submission history

[v1] 9 May 2011

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