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Pati-Salam model in curved space-time and sheaf quantization.

De-Sheng Li

This note aims to give a self-contain and detail explaination about U(k′) × U(k) Pati-Salam model in curved space-time which derived from (1 + n)-dimensional square root Lorentz manifold by self-parallel transportation principle. The concepts fundation of manifold from view point of category theory, fiber bundle and sheaf theories are reviewed. There are extra U(k′) × U(k)-principal bundle and U(k)-associated bundle than (1 + n)-dimensional Lorentz manifold. The conservative currents on square root Lorentz manifold is discussed preliminary. A detail proof of relation from sheaf quantization to path integral quantization is given.