12-dimensional Lie Algebra of Entangled Spin Fields

This result, that Dirac equation is equivalent with two entangled Proca fields with mass 2m and two constant massless fields, suggest that this representation unifies fermionic and bosonic fields, its algebra of 12 operators could be used for study of weak and strong interactions. While the gauge symmetry U(1)× SU(2)× SU(3) of the Standard Model is exact only when the particles are massless, the 12-dimensional Lie algebra proposed have the mass built in, i.e. it require neither cumbersome mechanism with arbitrary chosen fields and parameters nor spontaneous breaking symmetry to generate mass. In our model, the solutions of the equations Sα₁∂αSβ₂=0 and Sα₂∂αSβ₁=0 gives the mass of the field S₁αS¹α=-m² and S₂αS²α=-m². The 12-dimensional Lie algebra of entangled spin can be applied to Yang-Mills theory together with a set of $12$ massless spin fields, six of them described by S¹ and six by S², their interaction to generate mass will be the subject of a future study.