关于经典力学的辛约化
On Symplectic Reduction in Classical Mechanics
摘要：
本文阐述了有限维哈密顿力学的现代辛约化理论。这个理论推广了连续对称性和守恒量之间的著名联系，即诺特定理。它还阐明了力学的一个宏大主题：利用对称性来减少处理问题所需的变量数量。论述强调如何提供有关旋转组和刚体的理论见解。该理论对状态空间的描述也为哲学问题带来了启示，即两种明显不同但完全不可分辨的可能性是否应该被裁定为同一种。这些问题是用“关系主义”机制来说明的。
英文摘要：
This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It also illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emphasises how the theory provides insights about the rotation group and the rigid body. The theory's device of quotienting a state space also casts light on philosophical issues about whether two apparently distinct but utterly indiscernible possibilities should be ruled to be one and the same. These issues are illustrated using ``relationist'' mechanics.
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