论文标题
一个单一晶格仪理论的单粒子框架在离散时间内
A single-particle framework for unitary lattice gauge theory in discrete time
论文作者
论文摘要
我们为单个粒子的自旋1/2物质字段构建了实时晶格阶段理论型动作（1+1） - 维空间时空的晶格。该框架基于一个离散的量子步行，因此是固有的统一和严格局部的，即过渡幅度完全消失在晶格上的灯笼外。然后，我们为该动作的内部对称性提供了一个Noether定理。我们通过在晶格上的最小替代品将这一动作与电磁场相结合。最后，我们建议在任意时空维度中为电磁场的实时晶格规定型动作，并得出其经典运动方程，这是Maxwell方程的晶格版本。
We construct a real-time lattice-gauge-theory-type action for a spin-1/2 matter field of a single particle on a (1+1)-dimensional spacetime lattice. The framework is based on a discrete-time quantum walk, and is hence inherently unitary and strictly local, i.e., transition amplitudes exactly vanish outside of a lightcone on the lattice. We then provide a lattice Noether's theorem for internal symmetries of this action. We further couple this action to an electromagnetic field by a minimal substitution on the lattice. Finally, we suggest a real-time lattice-gauge-theory-type action for the electromagnetic field in arbitrary spacetime dimensions, and derive its classical equations of motion, which are lattice versions of Maxwell's equations.
