12-dimensional Lie Algebra of Entangled Spin Fields

This result, that Dirac equation is equivalent with two entangled Proca fields with mass $\mathsf{2m}$ 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 $U(1)\times SU(2)\times SU(3)$ 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 $S^{\alpha}_{1}\partial_{\alpha}S^{\beta}_{2}=0$ and $S^{\alpha}_{2}\partial_{\alpha}S^{\beta}_{1}=0$ gives the mass of the field $S_{1}^{\alpha}S^{1}_{\alpha}=-m^{2}$ and $S_{2}^{\alpha}S^{2}_{\alpha}=-m^{2}$. 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 $S^{1}$ and six by $S^{2}$, their interaction to generate mass will be the subject of a future study.