Covariant canonical gauge theory of gravitation for fermions

Understand

We 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.