论文标题
在Abelian仪表理论的紧张配方中连续对称的离散方面
Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories
论文作者
论文摘要
我们表明，具有$ u（1）$对称性的晶格模型的标准身份和定理在这些模型的张力公式中会离散地重新表达。我们解释了运动的连续晶格方程与张量的离散选择规则之间的几何类比。我们在任意维度中构建一个规数传输矩阵。我们以最大的时间表显示了与量规固定版本的等效性，并解释了如何始终执行离散的高斯定律。我们提出了一种噪音的方式，以任意维度实施高斯定律。我们针对全球，局部，连续或离散的Abelian对称性重新制定了Noether定理：对于每个给定的对称性，都有一个相应的张量冗余。我们讨论了在两种可解决的情况下具有周期性边界条件的经典解决方案的半古典近似值。我们显示了它们弱耦合极限与泊松求和后张量公式的对应关系。我们简要讨论了与其他方法的连接以及对量子计算的含义。
We show that standard identities and theorems for lattice models with $U(1)$ symmetry get re-expressed discretely in the tensorial formulation of these models. We explain the geometrical analogy between the continuous lattice equations of motion and the discrete selection rules of the tensors. We construct a gauge-invariant transfer matrix in arbitrary dimensions. We show the equivalence with its gauge-fixed version in a maximal temporal gauge and explain how a discrete Gauss's law is always enforced. We propose a noise-robust way to implement Gauss's law in arbitrary dimensions. We reformulate Noether's theorem for global, local, continuous or discrete Abelian symmetries: for each given symmetry, there is one corresponding tensor redundancy. We discuss semi-classical approximations for classical solutions with periodic boundary conditions in two solvable cases. We show the correspondence of their weak coupling limit with the tensor formulation after Poisson summation. We briefly discuss connections with other approaches and implications for quantum computing.
