Quaternionic spontaneous symmetry breaking and Weinberg-Salam model

Theory of spontaneous symmetry breaking is analyzed in terms of quaternions . Lagrangian density is written as a scalar quantity of quaternionic valued Function. For minimizing the potential V (phi) = mu (2)<(<phi>)over bar>ph i+lambda(<(<phi>)over bar>phi)(2) the vacuum expectations values <(<nu>)ove r bar>nu = -mu (2)/2 lambda are obtained in a consistent way. Quaternion va lued scalar lagrangian reduces four different field equations associated wi th scalar fields phi (0), phi (1), phi (2) and phi (3) of a quaternion phi = phi (0) + e(1)phi (1) + e(2)phi (2) + e(3)phi (3). Spontaneous breaking o f global and local gauge symmetries are analyzed by means of quaternions. I t is shown that the quaternion gauge group SO(4) is spontaneously broken to SO(4) approximate to SO(3) x SO(3) associated with two gauge field quantas . Quaternionic gauge theory is investigated as the composite stales of quar ks and leptons associated with vector and scaler part of quaternion valued fields, respectively. Weinberg-Salam SU(2) x U(1) gauge theory of electrowe ak interaction is extensively studied to enlarge the gauge group SU(2)(L) x SU(2)(R) x U(1).