从最大熵原理看四面体的统计平衡
Statistical equilibrium of tetrahedra from maximum entropy principle
摘要：
四维时空中的（量子）引力的离散公式用四面体构建空间。我们调查的统计力学系统的四面体从一个多体的角度来看，基于非本地的，组合胶合约束，建模为多粒子相互作用。我们专注于吉布斯平衡态，构造使用Jaynes的熵，这已被证明最近发挥了重要作用，在背景独立系统的平衡特征的原则。我们首先将这一原则应用于经典系统的许多四面体使用不同的例子几何动机的约束。然后，对于一个系统的量子四面体，我们表明，量子统计的吉布斯态的配分函数相对于一些约束算子可以重新解释为一个配分函数的量子场论的四面体，采取一个群场论的形式。
英文摘要：
Discrete formulations of (quantum) gravity in four spacetime dimensions build space out of tetrahedra. We investigate a statistical mechanical system of tetrahedra from a many-body point of view based on non-local, combinatorial gluing constraints that are modelled as multi-particle interactions. We focus on Gibbs equilibrium states, constructed using Jaynes' principle of constrained maximisation of entropy, which has been shown recently to play an important role in characterising equilibrium in background independent systems. We apply this principle first to classical systems of many tetrahedra using different examples of geometrically motivated constraints. Then for a system of quantum tetrahedra, we show that the quantum statistical partition function of a Gibbs state with respect to some constraint operator can be reinterpreted as a partition function for a quantum field theory of tetrahedra, taking the form of a group field theory.
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