论文标题
测量空间和尺寸的哈密顿力学
Measurand Spaces and Dimensioned Hamiltonian Mechanics
论文作者
论文摘要
在本文中，我们介绍了哈密顿力学的概括，该机械师代替了配置空间，通常简单地将其视为平滑的歧管，而线条捆在光滑的歧管上。然后将经典可观察物识别为这些（通常是非平地）线束的部分。这种概括在数学上用雅各比歧管理论阐明，是由对实践科学中测量和测量单位的数学基础的概念修改进行的。我们证明了喷气捆绑包上存在的接触结构的几个技术结果，以指出我们的提议确实成功地概括了哈密顿力学，同时纳入了对物理维度和单位的系统处理。
In this paper we introduce a generalization of Hamiltonian mechanics that replaces configuration spaces, conventionally regarded simply as smooth manifolds, with line bundles over smooth manifolds. Classical observables are then identified with the sections of these (generically non-trivial) line bundles. This generalization, mathematically articulated with theory of Jacobi manifolds, is motivated by a conceptual revision of the mathematical foundations of the notion of measurand and unit of measurement in practical science. We prove several technical results for the contact structures present on jet bundles in order to argue that our proposal does indeed successfully generalize Hamiltonian mechanics while incorporating a systematic treatment of physical dimension and units.
