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Abstract: Using complexified quaternions, an intriguing link between generators of twodifferent and surprisingly commuting four-dimensional representations of theSU2xU1 Lie group, and generators of two four-dimensional spin 1-2representations of the Spin3,1 Lie group is established: the formergenerators completely determine the latter ones, and cross-combined theyconstitute two different, but closely related, four-dimensional representationsof Spin3,1xSU2xU1. These representations are used to construct aSpin3,1xSU2xU1 gauge invariant Lagrangian, containing two four-spinorsconsisting not as usual of Weyl two-spinors of opposite helicity and equal weakisospin, but instead of Weyl two-spinors of opposite weak isospin and equalhelicity, a construction which arises naturally from the mathematical formalismitself. A possible future generalization, using complexified octonions, isdiscussed.



Author: John Fredsted

Source: https://arxiv.org/







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