圈量子引力的粗粒化模型及其重整化
Coarse-grained models for loop quantum gravity and their renormalization
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中文总结 AI 辅助
本研究为正则圈量子引力构建含两个参数的粗粒化模型，基于自旋网络态粗粒化过程推导有效哈密顿量，给出非微扰重整化框架与流方程，为研究连续极限涌现及唯象模型推导搭建了平台。
中文摘要 AI 辅助
我们引入一类有效理论，并利用它们为正则圈量子引力定义特定类型的粗粒化模型。每个有效理论由两个参数表征，主要包含粗粒化态的希尔伯特空间和有效哈密顿量算符。粗粒化希尔伯特空间的构建依赖于自旋网络态的系统粗粒化过程，而有效哈密顿量则通过分析该粗粒化过程与圈量子引力中各类哈密顿量算符作用的相互关系得到。最后，我们给出在粗粒化模型中实现哈密顿量非微扰重整化框架的方案，并明确写出重整化流方程。本工作的目标是构建一个研究正则圈量子引力中连续极限涌现及唯象模型推导的平台。
英文摘要
We introduce a family of effective theories and use them to define a specific type of coarse-grained models for canonical loop quantum gravity. Each effective theory is characterized by two parameters and it consists mainly of a Hilbert space of coarse states and an effective Hamiltonian operator. The construction of the coarse Hilbert spaces relies on a systematic coarse-graining procedure for spin network states. The effective Hamiltonians are then obtained from an analysis of the interplay between this coarse-graining procedure and the action of various Hamiltonian operators defined in loop quantum gravity. Finally, we provide a prescription for implementing the Hamiltonian non-perturbative renormalization framework for the coarse-grained models, and we explicitly write down the renormalization flow equations. The aim of this work is to build an arena for studying the emergence of the continuum limit and the derivation of phenomenological models in the context of canonical loop quantum gravity.
发表机构
- National Centre for Nuclear Research（国家核研究中心）
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