Spontaneous CP violation from a quaternionic Kaluza-Klein theory

Motivated by the isomorphism between the universal covering group of the six dimensional Lorentz group and the special linear group over the quaternions, a locally quaternionic covariant quantum mechanics is postulated to exist in six space-time dimensions. Compactifying onto the space-time M(exp 4) x S(exp 2) complex theory is retrieved on the four dimensional Minkowski space with the essential quaternionic nature confined to S(exp 2). Quaternionic spinors are introduced and a dimensionally reduced theory recovered which exhibits a CP violating effect via spontaneous symmetry breaking.