论文标题
离散线性典型进化
Discrete Linear Canonical Evolution
论文作者
论文摘要
这项工作建立在现有的离散典型演化模型的基础上，并将其应用于线性动力学系统的一般情况，即具有配置空间同构的有限维系统到$ \ MATHBB {R}^{Q} $ and Mational of Motion。假定系统在离散的时间步骤中演变。该模型最独特的特征是运动方程可能是不规则的。在对出现的约束和符号形式进行了分析之后，我们在相位空间上引入了调整后的坐标，该坐标揭示了其内部结构，并导致了哈密顿进化图的琐碎形式。为了说明，形式主义应用于二维时空晶格上无质量标量场的示例。
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.
