2018/09/30 by David Benisty, Eduardo Guendelman, Eduardo I. Guendelman +4
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical transformation #Conformal gravity #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Covariant transformation #Curvature #Gauge theory #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum mechanics #Riemann curvature tensor #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.98.106021
published as Phys. Rev. D 98, 106021 (2018) · 6 pages, 1 figure, last version before publishing in Phys Rev D
arxiv created 2018/11/13 · openalex publication_date 2018/11/26 · arxiv updated 2018/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The covariant canonical gauge theory of gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation framework are applied to derive a Palatini type gauge theory of gravity. The metric g_\ensuremathμ\ensuremathν, the affine connection \ensuremathγ^\ensuremathλ_\ensuremathμ\ensuremathν and their respective conjugate momenta, k^\ensuremathμ\ensuremathν\ensuremathσ and q_\ensuremathη^\ensuremathα\ensuremathξ\ensuremathβ tensors, are the independent field components describing the gravity. The metric is the basic dynamical field, and the connection is the gauge field. The torsion-free and metricity-compatible version of the spacetime Hamiltonian is built from all possible invariants of the q_\ensuremathη^\ensuremathα\ensuremathξ\ensuremathβ tensor components up to second order. These correspond in the Lagrangian picture to Riemann tensor invariants of the same order. We show that the quadratic tensor invariant is necessary for constructing the canonical momentum field from the gauge field derivatives, and hence for transforming between Hamiltonian and Lagrangian pictures. Moreover, the theory is extended by dropping metric compatibility and enforcing conformal invariance. This approach could be used for the quantization of the quadratic curvature theories, as for example in the case of conformal gravity.