Covariant canonical gauge theory of gravitation for fermions

  • 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. 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.

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Author:Jürgen StruckmeierORCiDGND, David VasakORCiD
Parent Title (German):Astronomische Nachrichten
Publisher:Wiley-VCH Verl.
Place of publication:Berlin
Document Type:Article
Date of Publication (online):2021/08/26
Date of first Publication:2021/08/26
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2021/11/15
Tag:canonical transformation; emerging mass parameter; extended Einstein gravity; fermion; gauge theory; gravitation; torsion
Page Number:20
First Page:745
Last Page:764
The authors are indebted to the “Walter Greiner-Gesellschaft e.V.” in Frankfurt for its support. DV is grateful for support from the Fueck Foundation. Open Access funding enabled and organized by Projekt DEAL.
Institutes:Wissenschaftliche Zentren und koordinierte Programme / Frankfurt Institute for Advanced Studies (FIAS)
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Licence (English):License LogoCreative Commons - Namensnennung-Nicht kommerziell 4.0