标题： 经典极限和非微扰量子引力中哈密顿约束的形式 显示英文标题

标题： The classical limit and the form of the hamiltonian constraint in nonperturbative quantum gravity

摘要： 有人认为，一些非微扰量子广义相对论的方法缺乏一个合理的连续极限，该极限无法重现广义相对论。 基本问题是，一般的物理态缺乏长程关联，因为态的形式允许将空间区域划分为不同的部分，使得一个区域中的物理态变化无法通过限制在另一区域的可观测量来测量。 这些不相连的区域通常具有有限的物理体积期望值，这意味着该理论没有长程关联或无质量粒子。 其中一个结果是，$ADM$能量在至少以自然的量子渐近平坦性概念和相应的测量$E_{ADM}$的算符定义时，从下方无界，这里给出了该算符的定义。 这些问题出现在Thiemann关于量子引力的新表述中。 其他一些方法，如Borissov、Rovelli和Smolin的方法中也出现了相关问题。 提出了一种新的哈密顿约束方法，可能可以避免缺乏长程关联的问题。 显示英文摘要

摘要： It is argued that some approaches to non-perturbative quantum general relativity lack a sensible continuum limit that reproduces general relativity. The basic problem is that generic physical states lack long ranged correlations, because the form of the state allows a division into spatial regions, such that no change in the physical state in one region can be measured by observables restricted to another. These disconnected regions have generically finite expectation value of physical volume, which means that the theory has no long ranged correlations or massless particles. One consequence of this is that the $ADM$ energy is unbounded from below, at least when that is defined with respect to a natural notion of quantum asymptotic flatness and a corresponding definition of an operator that measures $E_{ADM}$ (which is given here). These problems occur in Thiemann's new formulation of quantum gravity. Related issues arise in some other approaches such as that of Borissov, Rovelli and Smolin. A new approach to the Hamiltonian constraint, which may avoid the problem of the lack of long ranged correlations, is proposed.