General Relativistic Quantum Theories: Foundations, the Leptons Masses

Abstract

The space-time is represented by a usual, four-dimensional differential manifold, X. Then it is assumed that at every point x of X, we have a Hilbert space H(x) and a quantum description (states, observables, probabilities, expectations) based on H(x). The Riemannian structure of X induces a connection on the fiber bundle H and this assumption has many relevant consequences: the theory is regularized; the interaction energy is a well defined self-adjoint operator; finally, applying the theory to electro-weak interactions, we can obtain a “specter” of leptons masses (electron, muon, tau).