Foliation, Jet Bundle and Quantization of Einstein Gravity
Foliation, Jet Bundle and Quantization of Einstein Gravity
复制标题
叶理、射流束和爱因斯坦引力的量子化
作者：
I. Park
在 cite{Park:2014tia} 中，我们提出了一种在 ADM 设置中使用哈密顿量和拉格朗日分析来量化重力的方法。关键的观察结果之一是 4D 爱因斯坦-希尔伯特作用的物理配置空间允许三维描述，{从而通过度量场重新定义使重力重整化成为可能。}随后，在 cite{Park:2014qoa} 中提出了基于叶状理论的更数学化和补充性的简化图。通过叶状结构的设置，物理自由度已被确定为特定的叶子。在这里，我们通过添加另一个数学成分 - 射流束理论的一个元素来扩展 cite{Park:2014qoa} 的工作。随着射流束的引入，识别其中概述的真实自由度的过程变得精确，并且减少的整个图景被置于坚实的数学基础上。
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.
DOI：
10.4310/atmp.2013.v17.n6.a5
发表时间：
2012
期刊：
arXiv: General Relativity and Quantum Cosmology
影响因子：
--
作者：
Claus Gerhardt
通讯作者：
Claus Gerhardt