标题： 量子链模型：规范理论的离散方法 显示英文标题

标题： Quantum Link Models: A Discrete Approach to Gauge Theories

摘要： 我们构建了格点规范理论，其中链接矩阵的元素由作用在希尔伯特空间中的非对易算符表示。 这些量子链接模型与普通格点规范理论的关系，就如同量子自旋模型与普通经典自旋系统的关系一样。 这里具体构造了U(1)和SU(2)的量子链接模型。 作为哈密顿理论，量子链接模型是非相对论性的规范理论，具有在凝聚态物理中的潜在应用。 当用第五个欧几里得维度表述时，普遍性论证表明会发生维数约化到四维。 因此，量子链接模型也是普通量子场理论的重新表述，并适用于粒子物理，例如QCD。 量子链接模型的配置空间是离散的，因此它们的数值处理应该比具有连续配置空间的普通格点规范理论更简单。 显示英文摘要

摘要： We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as quantum spin models are related to ordinary classical spin systems. Here U(1) and SU(2) quantum link models are constructed explicitly. As Hamiltonian theories quantum link models are nonrelativistic gauge theories with potential applications in condensed matter physics. When formulated with a fifth Euclidean dimension, universality arguments suggest that dimensional reduction to four dimensions occurs. Hence, quantum link models are also reformulations of ordinary quantum field theories and are applicable to particle physics, for example to QCD. The configuration space of quantum link models is discrete and hence their numerical treatment should be simpler than that of ordinary lattice gauge theories with a continuous configuration space.