Covariant canonical gauge theory of gravitation for fermions

Abstract

AbstractWe derive the interaction of fermions with a dynamical space–time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form‐invariance of the fermion action under diffeomorphisms. The derivation is worked out in the Hamiltonian formalism as a canonical transformation along the line of non‐Abelian gauge theories. This yields a closed set of field equations for fermions, unambiguously fixing their coupling to dynamical space–time. We encounter, in addition to the well‐known minimal coupling, anomalous couplings to curvature and torsion. In torsion‐free geometries that anomalous interaction reduces to a Pauli‐type coupling with the curvature scalar via a spontaneously emerged new coupling constant with the dimension of mass. A consistent model Hamiltonian for the free gravitational field and the impact of its functional form on the structure of the dynamical geometry space–time is discussed.