Non-local boundary conditions in Euclidean quantum gravity
Non-local boundary conditions in Euclidean quantum gravity
复制标题
欧几里得量子引力中的非局域边界条件
DOI：
10.1088/0264-9381/16/4/002
复制
发表时间：
1998
影响因子：
3.5
通讯作者：
G. Esposito
中科院分区：
文献类型：
--
作者：
G. Esposito
提出了欧氏量子引力的非定域边界条件，该边界条件由作用于度量扰动的积分-微分边界算子组成。在这种情况下，算子P的度量扰动是拉普拉斯型，受非局部边界条件;相反，它的伴随是一个拉普拉斯算子和一个奇异绿色算子的总和，受局部边界条件。自伴性的边值问题是正确制定的Dirichlet型和Neumann型实现的运营商P，最近的结果在文献中。引力场微扰模的非局部边界条件集以一般形式写在欧氏四球上。对于一个特定的选择的非局部边界算子，显式公式的边界值问题得到的有限数量的未知函数，但受到一些一致性条件。在相关的问题中，欧几里德量子引力中是否存在非定域对称性的问题就出现了。
Non-local boundary conditions for Euclidean quantum gravity are proposed, consisting of an integro-differential boundary operator acting on metric perturbations. In this case, the operator P on metric perturbations is of Laplace type, subject to non-local boundary conditions; in contrast, its adjoint is the sum of a Laplacian and of a singular Green operator, subject to local boundary conditions. Self-adjointness of the boundary value problem is correctly formulated by looking at Dirichlet-type and Neumann-type realizations of the operator P, following recent results in the literature. The set of non-local boundary conditions for perturbative modes of the gravitational field is written in general form on the Euclidean 4-ball. For a particular choice of the non-local boundary operator, explicit formulae for the boundary value problem are obtained in terms of a finite number of unknown functions, but subject to some consistency conditions. Among the related issues, the problem arises of whether non-local symmetries exist in Euclidean quantum gravity.