Foliation, jet bundle and quantization of Einstein gravity

Abstract

In \cite{Park:2014tia} we proposed a way of quantizing gravity with the Hamiltonian and Lagrangian analyses in the ADM setup. One of the key observations was that the physical configuration space of the 4D Einstein-Hilbert action admits a three-dimensional description, thereby making gravity renormalization possible through a metric field redefinition. Subsequently, a more mathematical and complementary picture of the reduction based on foliation theory was presented in \cite{Park:2014qoa}. With the setup of foliation the physical degrees of freedom have been identified with a certain leaf. Here we expand the work of \cite{Park:2014qoa} by adding another mathematical ingredient - an element of jet bundle theory. With the introduction of the jet bundle, the procedure of identifying the true degrees of freedom outlined therein is made precise and the whole picture of the reduction is put on firm mathematical ground.

34 pages, 3 figures, sections restructured and two appendices added, comments on loop quantum gravity added, refs added, version to appear in Frontiers in Physics

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Cited by in corpus (10)

• Holographic quantization of gravity in a black hole background
• One-loop renormalization of a gravity-scalar system
• Boundary dynamics in gravitational theories
• Quantum-corrected geometry of horizon vicinity
• Foliation-based quantization and black hole information
• Foliation-based approach to quantum gravity and applications to astrophysics
• Reduction of gravity-matter and dS gravity to hypersurface
• 4D covariance of holographic quantization of Einstein gravity
• Quantization of gravity and finite temperature effects
• DeWitt boundary condition in one-loop quantum cosmology