标题： 高阶经典辛系统中的动力相似性 显示英文标题

标题： Dynamical Similarity in Higher-Order Classical Symplectic Systems

摘要： 许多具有哈密顿描述的物理相关理论，在一类称为动力相似性的非严格共形变换下表现出对称性。这种对称性的存在允许进行约化过程，从系统中消除一个自由度，我们将其与整体尺度相关联。这种“接触约化”过程导致了具有摩擦性质的理论，其中物理可观测量形成一个独立的子系统，以可预测的方式演化。我们证明该过程可以自然地推广到高阶理论；提供了详细的例子，并讨论了物理意义。 显示英文摘要

摘要： Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non -strictly conformal transformation, known as dynamical similarities. The presence of such symmetries allows a reduction process to be carried out, eliminating a single degree of freedom from the system, which we associate with an overall scale. This process of `contact reduction' leads to theories of a frictional nature, in which the physically-observable quantities form an autonomous subsystem, that evolves in a predictable manner. We demonstrate that this procedure has a natural generalisation to theories of higher order; detailed examples are provided, and physical implications discussed.