叶理、喷流丛与爱因斯坦引力的量子化
Foliation, jet bundle and quantization of Einstein gravity
摘要：
在\cite{Park:2014tia}中，我们提出了一种在ADM系统中用哈密顿量和拉格朗日量分析量子化引力的方法。其中一个关键的观察是，四维爱因斯坦-希尔伯特作用量的物理位形空间允许一个三维的描述，从而使引力重整化通过度量场的重新定义成为可能。随后，在\cite{Park:2014qoa}中提出了一个基于叶理理论的更加数学化和补充的还原图。随着叶理的建立，物理自由度已经被确定为特定的叶子。在这里，我们扩大了\cite{Park:2014qoa}的工作，增加了另一个数学成分-射流束理论的一个元素。随着射流束的引入，确定其中所概述的真实自由度的过程变得精确，并且将整个简化过程建立在坚实的数学基础上。
英文摘要：
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.
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