论文标题
一维晶格上的庞加莱水晶
Poincaré crystal on the one-dimensional lattice
论文作者
论文摘要
在本文中，我们开发了粒子的量子理论，该理论在一维勇敢的晶格上具有离散的庞加莱对称性。我们回顾了最近发现的离散Lorentz对称性，这是独特的Lorentz对称性，它与Bravais晶格上离散的空间翻译对称性并存。离散的Lorentz转换和时空翻译形成了离散的Poincaré群体，在量子理论中由单一操作员代表。我们发现了代表的存在条件，这些条件表示为准摩托明和准能量之间的一致性关系。然后，我们通过用现场操作员来表达单一操作员和浮标的汉密尔顿人来构建无法区分的粒子的多体型理论。一些典型的汉密尔顿人包括远距离跳跃，随着站点之间的距离的增加而波动。我们计算晶格理论的绿色功能。绿色函数非零的时空点显示晶格结构。在传播过程中，颗粒保持位于单个或几个位点以保留Lorentz对称性。
In this paper, we develop the quantum theory of particles that has discrete Poincaré symmetry on the one-dimensional Bravais lattice. We review the recently discovered discrete Lorentz symmetry, which is the unique Lorentz symmetry that coexists with the discrete space translational symmetry on a Bravais lattice. The discrete Lorentz transformations and spacetime translations form the discrete Poincaré group, which are represented by unitary operators in a quantum theory. We find the conditions for the existence of representation, which are expressed as the congruence relation between quasi-momentum and quasi-energy. We then build the Lorentz-invariant many-body theory of indistinguishable particles by expressing both the unitary operators and Floquet Hamiltonians in terms of the field operators. Some typical Hamiltonians include the long-range hopping which fluctuates as the distance between sites increases. We calculate the Green's functions of the lattice theory. The spacetime points where the Green's function is nonzero display a lattice structure. During the propagation, the particles stay localized on a single or a few sites to preserve the Lorentz symmetry.
