V2EX path integral

Path Integral

Definition / 定义

路径积分:量子力学与量子场论中的一种表述方法,把粒子从初态到末态的演化看作对“所有可能路径/历史”的贡献进行加权求和(或在连续极限下的积分)。最常见的是费曼路径积分,权重通常与作用量 \(S\) 相关(如 \(e^{iS/\hbar}\))。

Pronunciation / 发音

/pθ ntrl/

Examples / 例句

The path integral gives an alternative way to compute the quantum amplitude.
路径积分提供了一种计算量子振幅的替代方法。

Using the path integral formalism, one can derive correlation functions by integrating over all field configurations with appropriate boundary conditions.
使用路径积分形式体系,可以通过对所有满足合适边界条件的场构型进行积分来推导关联函数。

Etymology / 词源

path(路径)+ integral(积分)。该术语在物理语境中因理查德费曼(Richard Feynman)在 20 世纪中期发展“对所有路径求和”的量子力学表述而广为流行,因此常与 Feynman path integral(费曼路径积分)并称。日常数学里的“积分”概念被借用来表达对连续无穷多“可能历史”的汇总。

Related Words / 相关词

Literary Works / 文学作品

  • Richard P. Feynman, The Space-Time Approach to Non-Relativistic Quantum Mechanics(提出并系统阐述路径积分思想的经典论文)
  • Richard P. Feynman & Albert R. Hibbs, Quantum Mechanics and Path Integrals(路径积分的代表性专著)
  • Steven Weinberg, The Quantum Theory of Fields(在量子场论框架中大量使用路径积分语言)
  • Michael E. Peskin & Daniel V. Schroeder, An Introduction to Quantum Field Theory(以路径积分与费曼图为核心工具的经典教材)
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