Covariant canonical gauge theory of gravitation for fermions

TL;DR

This paper develops a covariant canonical gauge theory of gravitation that unifies fermion interactions with dynamical spacetime, revealing novel anomalous couplings to curvature and torsion within a Hamiltonian framework.

Contribution

It introduces a new Hamiltonian formalism for fermion-gravity coupling, uncovering anomalous interactions and a spontaneously generated coupling constant in torsion-free geometries.

Findings

Unveiled anomalous fermion couplings to curvature and torsion.

Derived a closed set of field equations for fermion and gravitational interactions.

Identified a new coupling constant with mass dimension emerging spontaneously.

Abstract

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. 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 resp.\ inverse length. 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.