V2EX symplectic

Symplectic

释义 Definition

(数学/物理)辛的;辛几何的;与“辛结构/辛形式(symplectic form)”有关的。常用于描述一种在相空间中保持特定几何结构(典型地与哈密顿力学相关、可理解为“保持面积/体积的特殊结构”)的性质,如 symplectic manifold(辛流形)、symplectic transformation(辛变换)。

发音 Pronunciation (IPA)

/smplk.tk/

例句 Examples

A symplectic map preserves the symplectic form.
辛映射会保持辛形式不变。

Symplectic geometry provides the natural language for Hamiltonian mechanics and the study of phase space.
辛几何为哈密顿力学以及相空间的研究提供了自然的语言框架。

词源 Etymology

symplectic 源自较新的科学术语构词,来自 **sym-**(“共同、一起”)+ -plectic(与“编织/交织”相关的构词成分,源自希腊语词根),整体带有“交织在一起的结构”的意味。该词由数学家在研究经典力学的几何结构时推广,用来指代与“辛形式”相关、并保持这种结构的对象与性质。

相关词 Related Words

文学与名著用例 Literary Works

  • Vladimir I. Arnold, Mathematical Methods of Classical Mechanics(大量使用 symplectic 来讨论相空间与正则结构)
  • Ralph Abraham & Jerrold E. Marsden, Foundations of Mechanics(以辛几何表述经典力学框架)
  • Ana Cannas da Silva, Lectures on Symplectic Geometry(系统介绍辛几何的核心概念与例子)
  • Dusa McDuff & Dietmar Salamon, Introduction to Symplectic Topology(在辛拓扑语境中高频出现该词)
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