Covariant canonical gauge theory of gravitation for fermions

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.

arXiv comment21 pages

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Cited by in corpus (5)

• The dark side of the torsion: Dark Energy from propagating torsion
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• On the cosmological constant in the deformed Einstein-Cartan gauge gravity in De Donder-Weyl Hamiltonian formulation
• Identity for scalar-valued functions of tensors and its applications to energy-momentum tensors in classical field theories and gravity
• Pauli-type coupling between spinors and curved spacetime