This work builds on an existing model of discrete canonical evolution and applies it to the case of a linear dynamical system, i.e., a finite-dimensional system with vector configuration space 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 a massless scalar field on a two-dimensional spacetime lattice.

中文翻译：

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离散线性正则演化

这项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情况，即具有矢量配置空间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。该模型最显着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，这揭示了其内部结构并产生了哈密顿演化图的简单形式。为了说明，形式主义被应用于二维时空格子上的无质量标量场的例子。