TY - JOUR

T1 - Quadratic curvature theories formulated as covariant canonical gauge theories of gravity

AU - Benisty, David

AU - Guendelman, Eduardo I.

AU - Vasak, David

AU - Struckmeier, Jurgen

AU - Stoecker, Horst

N1 - Funding Information:
D. B. thanks Margarethe Puschmann and the Herbert Puschmann Stiftung for FIAS in the Verein der Freunde and Foerderer der Goethe University. D. V. thanks the Carl-Wilhelm Fueck Stiftung for generous support through the Walter Greiner Gesellschaft (WGG) zur Foerderung der physikalischen Grundlagenforschung Frankfurt. E. I. G. and D. B. are grateful for the support of COST Action CA15117 “Cosmology and Astrophysics Network for Theoretical Advances and Training Action” (CANTATA) of the European Cooperation in Science and Technology (COST). H. S. thanks the WGG and Goethe University for support through the Judah Moshe Eisenberg Laureatus endowed professorship and the BMBF (German Federal Ministry of Education and Research).
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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 gμν, the affine connection γλμν and their respective conjugate momenta, kμνσ and qηαξβ 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 qηαξβ 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.

AB - 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 gμν, the affine connection γλμν and their respective conjugate momenta, kμνσ and qηαξβ 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 qηαξβ 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.

UR - http://www.scopus.com/inward/record.url?scp=85057819044&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.98.106021

DO - 10.1103/PhysRevD.98.106021

M3 - Article

AN - SCOPUS:85057819044

VL - 98

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 10

M1 - 106021

ER -