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.

中文翻译：

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经典哈密顿场论的协变约简：从 D'Alembert 到 Klein-Gordon 和 Schrödinger

提出了一种新的协变经典场论归约程序，它反映了哈密顿系统的广义辛归约理论。这个简化过程的出发点在于选择描述场论的方程的解流形的子流形。然后，所涉及的几何对象的协方差将允许在缩减空间上定义运动方程。通过使用协变场论的多辛描述所提供的几何框架，可以巧妙地执行规范几何结构的计算。该过程通过将五维 Minkowski 时空的达朗贝尔理论简化为四维的大质量克莱因-戈登理论，更有趣的是，简化为 3 + 1 维的薛定谔方程来说明。