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 infinitesi-mal 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 non-associative octonionic ternary gauge field theory. These octonionc 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 Noncommu-tative and Nonassociative Geometry