用垂直投影的Gunther多辛形式主义的一个全球版本
A global version of Gunther's polysymplectic formalism using vertical projections
摘要：
我构造了一个整体版本的局部多辛方法的协变哈密顿场论开创的C。甘瑟从理论的几何框架开始，我专门研究垂直向量场来构造（多）辛结构，推导出Hamilton场方程，并构造一个或多或少的自然泊松括号。然后，我检查了几个关键的例子，以确定必要的垂直投影的性质，并发现该理论提供了几何模拟的正则变换方法协变哈密顿场论先进的Struckmeier和Redelbach。最后，我对这个框架在经典场论的几何量子化中的可能应用作了一些评论。
英文摘要：
I construct a global version of the local polysymplectic approach to covariant Hamiltonian field theory pioneered by C. Gunther. Beginning with the geometric framework of the theory, I specialize to vertical vector fields to construct the (poly)symplectic structures, derive Hamilton's field equations, and construct a more-or-less natural Poisson bracket. I then examine a few key examples to determine the nature of the necessary vertical projections and find that the theory provides the geometric analog of the canonical transformation approach to covariant Hamiltonian field theory advanced by Struckmeier and Redelbach. I conclude with a few remarks about possible applications of this framework to the geometric quantization of classical field theories.
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