论文标题
基于离散组的交叉模块对Yetter模型的动态概括
Dynamical generalization of Yetter's model based on a crossed module of discrete groups
论文作者
论文摘要
我们基于可能非亚伯有限基团的交叉模块构建动力学晶格模型。它的自由度定义在链接和斑点上，而规格的转换基于基础晶格的顶点和链接。我们指定了希尔伯特空间，定义了基本可观察物（包括哈密顿量），并启动了对模型相图的讨论。构造的模型概括了，并在适当的范围内降低了拓扑理论，其对称性由组和交叉模块，晶格阳米尔斯理论和2美元的型电动力学描述。最后，我们通过审查了交叉模块的分类空间，重点是它们的几何形状与所考虑的规格理论的性质之间的直接关系。
We construct a dynamical lattice model based on a crossed module of possibly non-abelian finite groups. Its degrees of freedom are defined on links and plaquettes, while gauge transformations are based on vertices and links of the underlying lattice. We specify the Hilbert space, define basic observables (including the Hamiltonian) and initiate a~discussion on the model's phase diagram. The constructed model generalizes, and in appropriate limits reduces to, topological theories with symmetries described by groups and crossed modules, lattice Yang-Mills theory and $2$-form electrodynamics. We conclude by reviewing classifying spaces of crossed modules, with an emphasis on the direct relation between their geometry and properties of gauge theories under consideration.
