Clifford algebra automorphisms in Theoretical Physics

The present investigation is a return to an old, and yet open, discussion about the relation between gravitational and weak interactions. Pauli’s conjecture on the possibility of new physics being related to the square root of the gravitational constant is addressed. A particular framework were gravity is induced by four-fermions is formulated. A general analysis of the internal consistency of spin connections in Riemannian geometry is considered, with special attention to the arbitrariness entailed by the Fock connection. In particular, the Fock connection is a non-Abelian gauge field of the Clifford bundle. We propose, as a possible synthesis of this analysis, that new degrees of freedom may arise from the group of automorphisms of the associated Clifford bundle. If this theory results internally consistent, a new framework embracing the electroweak model and sterile neutrinos coupled to gravity is envisaged, without changing the (external) properties of the physical spacetime.