论文标题
一阶的溶液空间哈密顿田间理论的几何形状I：从粒子动力学到自由电动力学
The Geometry of the solution space of first order Hamiltonian field theories I: from particle dynamics to free Electrodynamics
论文作者
论文摘要
我们分析了将泊松支架结构定义在一阶汉密尔顿现场理论方程的解决方案方程的空间上的问题。通过在溶液空间上显示出存在的符号结构（，因此也是泊松结构），可以解决哈密顿机械点系统（作为（0 + 1） - 维领域）和更一般的磁场理论的案例。同样，考虑到量规理论的最简单情况，即自由电动力学：在此问题中，引入了溶液空间上的隔透明张量，并且在与该理论相关的合适束上的平坦连接中引起了泊松结构。
We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems (as a (0 + 1)-dimensional field) and more general field theories without gauge symmetries are addressed by showing the existence of a symplectic (and, thus, a Poisson) structure on the space of solutions. Also the easiest case of gauge theory, namely free electrodynamics, is considered: within this problem, a pre-symplectic tensor on the space of solutions is introduced, and a Poisson structure is induced in terms of a flat connection on a suitable bundle associated to the theory.
