AI 中文总结
本文在2+1维U(1)格点规范理论中，证明修正高斯定律对应缺陷希尔伯特空间，构造磁平移算子并揭示其代数，并通过晶格对偶在紧致玻色子中体现修正定律。
AI 中文摘要
在哈密顿格点规范理论中，物理希尔伯特空间由高斯定律固定，即选择生成规范变换的高斯定律算子的一个本征空间。选择非平凡本征空间被称为修正高斯定律。在2+1维动力学U(1)纯规范理论中，我们证明这些物理希尔伯特空间是缺陷希尔伯特空间，与沿时间方向插入的磁单极子算子的非拓扑单值缺陷以及U(1) 1-形式对称性的拓扑缺陷相关联。我们还构造了相应的晶格平移算子。在非平凡修正高斯定律下，这些平移满足磁平移代数。最后，我们讨论了修正高斯定律如何通过晶格上的精确对偶在2+1维紧致玻色子中体现。
英文摘要
In a Hamiltonian lattice gauge theory, the physical Hilbert space is fixed by the Gauss law, by choosing an eigenspace of the Gauss law operator which generates the gauge transformation. Choosing a non-trivial eigenspace is referred to as the modified Gauss law. In 2+1d dynamical U(1) pure gauge theory, we show that these physical Hilbert spaces are defect Hilbert spaces associated with non-topological monodromy defects for monopole operators and topological defects for U(1) 1-form symmetry, inserted along the time direction. We also construct the corresponding lattice translation operators. Under a nontrivially modified Gauss law, these translations obey a magnetic translation algebra. Finally, we discuss how the modified Gauss laws are manifested in 2+1d compact bosons, via exact duality on the lattice.
Comments32 pages, 8 figures
