量子场论中的量子运动方程与量子诺特定理
Quantum Equation of Motion and Quantum Noether’s Theorem in Quantum Field Theory
摘要: 运动方程和诺特定理是经典场论中的核心概念。然而在实际的量子场论中，需要使用量子运动方程和量子诺特定理来研究一系列与物理观测量相关的关联函数或者矩阵元。经典场论中的运动方程和诺特定理与其量子版本之间具有非常微妙，但却十分重要的联系与区别。透析这一点，无论对于前沿工作者，抑或是初学场论的研究生，都具有非常重要的意义。它揭示了经典物理与量子物理之间的本质差别。本文利用路径积分量子化方法，从第一性原理出发，基于泛函计算体系，推导出了量子版本的运动方程与诺特定理，详细探讨了其与经典版本之间的联系与区别。这对于量子物理的前沿计算具有重要的指导和规范作用，也为初学场论的研究生快速进入前沿领域的研究，提供了一条脉络清晰，可操作性很强的道路。
Abstract: Equation of motion and Noether’s theorem are core concepts in classical field theory. However, in practical quantum field theory, it is necessary to use quantum equation of motion and quantum Noether’s theorem to study a series of correlation functions or matrix elements related to physical observables. There is a very subtle yet crucial connection and difference between the classical and quantum versions of the equation of motion and Noether’s theorem. Analyzing this is of great importance not only for researchers at the forefront but also for graduate students new to field theory. It reveals the fundamental differences between classical and quantum physics. This paper utilizes the path integral quantization method, starting from first principles, based on functional calculation, to derive the quantum versions of the equations of motion and Noether’s theorem, and it thoroughly discusses their connections and differences with the classical versions. This serves as an important guide and standard for frontier calculations in quantum physics and also provides a clear and practical path for graduate students new to field theory to quickly engage in forefront research.
文章引用：庞锦毅. 量子场论中的量子运动方程与量子诺特定理[J]. 物理化学进展, 2024, 13(4): 762-771. https://doi.org/10.12677/japc.2024.134076

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