Discrete linear canonical evolution

Jakub K'aninsk'y
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引用次数: 1

Abstract

This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear equations of motion. The system is assumed to evolve in discrete time steps. The most distinctive feature of the model is that the equations of motion can be irregular. After an analysis of the arising constraints and the symplectic form, we introduce adjusted coordinates on the phase space which uncover its internal structure and result in a trivial form of the Hamiltonian evolution map. For illustration, the formalism is applied to the example of massless scalar field on a two-dimensional spacetime lattice.
离散线性正则演化
本工作建立在现有的离散正则演化模型的基础上,并将其应用于线性动力系统的一般情况,即具有构型空间同构于$ \mathbb{R}^{q} $和线性运动方程的有限维系统。假设系统以离散时间步长演化。该模型最显著的特点是运动方程可以是不规则的。在分析了产生的约束和辛形式之后,我们在相空间上引入了调整坐标,揭示了相空间的内部结构,得到了哈密顿演化图的平凡形式。为了说明这一形式,将其应用于二维时空点阵上的无质量标量场的例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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