Bosons and Fermions : Quantum Defects in Einstein-Cartan Spacetime

By linearizing the Bianch Indentities we obtain conservation laws where torsion gradients yield conserved symmetric and anti-symmetric curvature and metrics, i.e. gravitational fields. In discrete spacetime, Regge calculus, curvature is localised on the 2-simplex disclination end, representing a rotational defect, with energy–momentum along its legs, with torsion representing translational defects,i.e. dislocations. Davies (1997) proved a baryon of three quarks corresponds to a triangular 2-simplex. Gauge approaches that include torsion show the equivalence to quantum field theory. In Feynman diagrams, particle lines meet at vertices where energy, momentum, and charge are conserved with torsion dislocations, bosons, terminating in curvature disclinations, fermions. Linear Bianchi identities yield the electroweak equations and for strong fields, the non-linear identities are equivalent to the Yang-Mills equations. Torsion, manifesting as bosons, proves the quantum Einstein-Cartan Universe.