Relativistic Fermion and Boson Fields: Bose-Einstein Condensate as a Time Crystal

In a basis of the space-time coordinate frame four quaternions discovered by Hamilton can be used. For subsequent reproduction these are expanded to 4 × matrices with real-valued matrix coefficients ?0 and 1. This group set is isomorphic SU(2) group. Such introduces extra six degrees freedom matter motion in space-time. There three rotations about space axes boosts along axes. Next one declares differential generating operators acting on energy-momentum density tensor written above quaternion basis. The actions this operator together its transposed lead emergence gravitomagnetic equations that like Maxwell equations. Wave extracted from ones describe propagation energy waves their vortices through space. Dirac reduction two functions, quantum Hamilton-Jacobi continuity equations, considered. Klein-Gordon arising mass shell hints alternation paired fermion fields boson ones. As an example, Feynman diagram electron–positron time crystal illustrated.