论文标题
古典汉密尔顿现场理论的协变量：从D'Anembert到Klein-Gordon和Schrödinger
Covariant reduction of classical Hamiltonian Field Theories: From D'Alembert to Klein-Gordon and Schrödinger
论文作者
论文摘要
介绍了一个新的减少经典田地理论，反映了汉密尔顿体系的广义象征性还原理论。此还原过程的出发点包括选择描述场理论的方程式解决方案的歧管。然后，所涉及的几何对象的协方差将允许在减少空间上定义运动方程。通过使用协方差田间理论的多连结膜描述提供的几何框架，可以整齐地进行规范几何结构的计算。通过将五维Minkowski时空的D'Alembert理论降低到四个维度的巨大的Klein-Gordon理论来说明该过程，更有趣的是，更有趣的是，在3+1个维度中更有趣的是Schrödinger方程。
A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction procedure consists in the choice of a submanifold of the manifold of solutions of the equations describing a field theory. Then, the covariance of the geometrical objects involved, will allow to define equations of motion on a reduced space. The computation of the canonical geometrical structure is performed neatly by using the geometrical framework provided by the multisymplectic description of covariant field theories. The procedure is illustrated by reducing the D'Alembert theory on a five-dimensional Minkowski space-time to a massive Klein-Gordon theory in four dimensions and, more interestingly, to the Schrödinger equation in 3+1 dimensions.
