Pati-Salam Model in Curved Space-Time from Square Root Lorentz Manifold

There is a ( ) 4' 4 UU × -bundle on four-dimensional square root Lorentz manifold. Then Pati-Salam model in curved space-time (Lagrangian) and gravity theory are constructed manifold based self-parallel transportation principle. An explicit formulation of Sheaf quantization this shown. superposition principle construct linear space space-time. The transition amplitude path integral given which consistent with quantization. All particles fields Standard Model (SM) particle physics Einstein found metric the connections bundle. interactions between particles/fields described by Lagrangian explicitly. few new model. Einstein-Cartan kind torsion. particles, right handed neutrinos, dark photon, Fiona, c X ± 01212 ** ,, Y YY