Yang-Mills field from quaternion space geometry, and its Klein-Gordon representation

Summary: "An analysis of covariant derivatives of vectors in quaternion (Q-) spaces, performed using a Q-unit spinor-splitting technique and an {rm SL}(2,bf C)-invariance of quaternion multiplication, reveals a close connexion between Q-geometry objects and Yang-Mills (YM) field characteristics. In particular, it is shown that the Q-connexion (with quaternion non-metricity) and the related curvature of 4-dimensional (4D) space-times with 3D Q-space sections are formally equivalent to, respectively, the YM-field potential and field strength, traditionally emerging from the minimal action assumption. Plausible links between the YM field equation and the Klein-Gordon equation, in particular via its known isomorphism with the Duffin-Kemmer equation, are also discussed."