有效约束聚合理论及其连续极限
Effective constrained polymeric theories and their continuum limit
摘要：
聚合物量子理论的经典极限产生了一个用λ标记的单参数“有效”理论族。在这里，我们考虑这样的家庭的约束理论和提出的问题，采取“连续极限”，λ-> 0。我们提出了这样的问题是很好地提出的标准，并提出了一个具体的战略的基础上，适当构造狄拉克可观的定义。我们详细分析了两个模型，即一个约束振子和一个宇宙模型所产生的圈量子宇宙学。对于这两个模型，我们表明，该计划确实可以完成，提供一个特定的选择λ依赖的内部时间，相对于动态描述和比较。我们证明了极限理论的存在并讨论了相应的极限。这些结果可能有助于解决量子约束系统的重整化群方法及其相关的连续极限的定义问题。
英文摘要：
The classical limit of polymer quantum theories yields a one parameter family of `effective' theories labeled by λ. Here we consider such families for constrained theories and pose the problem of taking the `continuum limit', λ-> 0. We put forward criteria for such question to be well posed, and propose a concrete strategy based in the definition of appropriately constructed Dirac observables. We analyze two models in detail, namely a constrained oscillator and a cosmological model arising from loop quantum cosmology. For both these models we show that the program can indeed be completed, provided one makes a particular choice of λ-dependent internal time with respect to which the dynamics is described and compared. We show that the limiting theories exist and discuss the corresponding limit. These results might shed some light in the problem of defining a renormalization group approach, and its associated continuum limit, for quantum constrained systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
