论文标题
量子系统离散线性演化的模型
Models of Discrete Linear Evolution for Quantum Systems
论文作者
论文摘要
离散的典型演化是理解时空离散模型中的动力学的关键工具，尤其是由三角形雷格晶格表示的动力学。我们考虑了一个有限维系统，该系统通过一系列由汉密尔顿运动方程式控制的离散时间进化步骤实现，该步骤在规范坐标中是线性的。允许进化是不规则的，这会产生约束和解决方案的非唯一性。我们为该系统的规范量化提供了两种独立且根本不同的方法，包括对进化图，测量和路径积分的详细描述。有人认为，某些不规则的离散系统可能是通过非自然量子进化最自然地描述的。然后将形式主义应用于二维时空晶格上的简单但与物理相关的无质量标量场模型。
Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by a series of discrete-time evolution steps governed by Hamiltonian equations of motion that are linear in the canonical coordinates. The evolution is allowed to be irregular, which produces constraints as well as non-uniqueness of solutions. We provide two independent and fundamentally different approaches to canonical quantization of this system, including detailed description of the evolution maps, measurement and path integrals. It is argued that some irregular discrete systems may be most naturally described by a non-unitary quantum evolution. The formalism is then applied to a simple yet physically relevant model of massless scalar field on a two-dimensional spacetime lattice.
