A systematic approach is developed in order to obtain spherically symmetric midisuperspace models that accept holonomy modifications in the presence of matter fields with local degrees of freedom. In particular, starting from the most general Hamiltonian quadratic in radial derivatives of the variables, we obtain a family of effective modified constraints that satisfy Dirac’s deformation algebra, which encodes the covariance of general relativity, and show that (scale-dependent) holonomy corrections can be consistently implemented. In vacuum, the deformed anomaly-free Hamiltonian is explicitly written in terms of three free functions and we obtain a weak observable that can be interpreted as the mass of the model. Finally, as a particular example, we present a specific covariant polymeric model that remains regular for any value of the connection components. Some of its physical implications and the relation with previous studies in the literature are commented upon.

中文翻译：

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与物质耦合的球面广义相对论的无异常变形

开发了一种系统的方法以获得球对称的 midisuperspace 模型，该模型在具有局部自由度的物质场的存在下接受完整的修改。特别是，从变量径向导数中最一般的哈密顿二次方程开始，我们获得了一系列满足狄拉克变形代数的有效修正约束，该代数编码广义相对论的协方差，并表明（与尺度相关的）完整修正可以始终如一地执行。在真空中，变形的无异常哈密顿量被明确地写成三个自由函数，我们获得了一个弱可观测量，可以解释为模型的质量。最后，作为一个特殊的例子，我们提出了一个特定的协变聚合模型，该模型对于连接组件的任何值都保持规则。评论了它的一些物理含义以及与以前文献中的研究的关系。