经典场论中的场重定义及若干量子视角
Field Redefinitions in Classical Field Theory with some Quantum Perspectives
AI总结：
本文在经典层面研究场重定义对可观测量、运动方程解及初边值条件的影响，给出LSZ公式的经典类比，并讨论不可逆重定义在孤子等非微扰对象下的局限。
摘要：
在量子场论中，场重定义常被用来去除拉格朗日量中的冗余算符，从而使计算更简单、物理更清晰。该技术需要谨慎处理诸多问题，包括可观测量的选择、适用范围以及运动方程（EOM）解的出现与消失。其中许多问题已经可以在经典层面进行研究，这正是本工作的重点。我们强调选择适当可观测量和初值/边界条件以确保解的物理不变性的重要性。给出了 Lehmann-Symanzik-Zimmermann（LSZ）公式的经典类比，证实某些可观测量在无需追踪重定义的情况下仍与场变量无关。此外，我们通过一个例子讨论了不可逆场重定义的局限性，特别是涉及孤子等非微扰对象时，并探讨了它们对经典和量子场论的影响。
英文摘要：
In quantum field theories, field redefinitions are often employed to remove redundant operators in the Lagrangian, making calculations simpler and physics more evident. This technique requires some care regarding, among other things, the choice of observables, the range of applicability, and the appearance and disappearance of solutions of the equations of motion (EOM). Many of these issues can already be studied at the classical level, which is the focus of this work. We highlight the importance of selecting appropriate observables and initial/boundary conditions to ensure the physical invariance of solutions. A classical analogue to the Lehmann-Symanzik-Zimmermann (LSZ) formula is presented, confirming that some observables remain independent of field variables without tracking redefinitions. Additionally, we address, with an example, the limitations of non-invertible field redefinitions, particularly with non-perturbative objects like solitons, and discuss their implications for classical and quantum field theories.
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