Quaternionic Weinberg-Salam Theory

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Abstract
A quaternionic Weinberg-Salam theory is formulated based on the assumption that fermions and Higgs mesons are defined over quaternions. The new formalism, reproducing the left-right symmetric SU(2)L × SU(2)R × U(1) Weinberg-Salam theory at the phenomenological level, offers an algebraic explanation for replication of quarks and leptons in flavor doublets, and correlates the spontaneous symmetry breakdown to U(1)em with the existence of Fock space for gauge singlets but not for quaternionic states. In particular, the quaternionic variational principle is introduced to canonically quantize the quaternionic fields in conformity with the gauge-singlet Fock-space formulation and the spontaneous symmetry breakdown. Physical states must be gauge singlets since they belong to the Fock space.

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