Foliation, Jet Bundle and Quantization of Einstein Gravity

Frontiers in Physics

Park, I. Y.¹ 

[1] Department of Physics, Hanyang University, Seoul, South Korea

关键词: ADM formalism;    Lagrangian and Hamiltonian reduction;    Foliation;    Jet bundle;    Quantization of gravity;    Holography;   

DOI  :  10.3389/fphy.2016.00025

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY