Octonionic ternary gauge field theories revisited

An octonionic ternary gauge field theory is explicitly constructed based on a ternary-bracket defined earlier by Yamazaki. The ternary infinitesimal gauge transformations do obey the key closure relations [δ1, δ2] = δ3. An invariant action for the octonionic-valued gauge fields is displayed after solving the previous problems in formulating a nonassociative octonionic ternary gauge field theory. These octonionic ternary gauge field theories constructed here deserve further investigation. In particular, to study their relation to Yang–Mills theories based on the G2 group which is the automorphism group of the octonions and their relevance to noncommutative and nonassociative geometry.

GRADED LIE ALGEBRA AND THE SU(3)L⊗U(1)N GAUGE MODEL

A classical gauge model based on the Lie group SU (3)L⊗ U (1)N with exotic quarks is reformulated within the formalism of nonassociative geometry associated with an L cycle. The N charges of the fermionic particles and the related parameter constraints are algebraic consequences and are uniquely determined. Moreover, the number of scalar particles is dictated by the nonassociativity of the geometry. As a byproduct of this formalism, the Weinberg angle θw, scalar, charged and neutral gauge boson masses, as well as the mixing angles, are derived. Furthermore, various expressions for the vector and axial couplings of the quarks and leptons with the neutral gauge bosons and lower bounds of the very heavy gauge bosons are obtained.