论文标题
Gunther使用垂直预测的全球版本的多链形式主义
A global version of Gunther's polysymplectic formalism using vertical projections
论文作者
论文摘要
我为C. Gunther启用的协变汉顿田间理论构建了局部多核方法的全球版本。从理论的几何框架开始，我专门研究垂直矢量场来构建（poly）符号结构，推导汉密尔顿的场方程，并构建一个或多或少的自然泊松支架。然后，我研究了一些关键示例，以确定必要的垂直投影的性质，并发现该理论提供了典范转换方法的几何类似物，用于由Struckmeier和Redelbach提出的协方差汉密尔顿场理论。我以一些关于该框架在经典田地理论的几何量化上的应用的评论进行了一些评论。
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.
