相对论量子理论与弯曲时空中的算符级量子-经典对应

中文摘要 AI 辅助

在近期工作\cite{Shaikh:2026nsi}中，已证明对于非相对论性粒子，算符运动方程可以写成与牛顿运动方程相同的微分形式。这就在运动方程层面建立了量子算符动力学与经典力学之间的对应关系。在本工作中，我们研究这种对应关系是否扩展到量子场论和线性化引力。我们明确证明，对于一大类场论，量子场算符的海森堡运动方程重现了相应的经典运动方程。克莱因-戈登方程、麦克斯韦方程、杨-米尔斯方程和线性化爱因斯坦方程被证明在算符层面出现，而无需取极限$\hbar\rightarrow0$。然后我们将分析扩展到弯曲时空，并证明量子场算符在算符层面满足相应的协变场方程。在弱场近似下，我们证明度规微扰的海森堡演化在算符层面重现线性化爱因斯坦方程。对于弯曲时空中的量子粒子，位置和动量的海森堡方程在半经典极限下重现经典测地运动，从而将算符级量子-经典对应从场论扩展到粒子动力学。

英文摘要

In a recent work \cite{Shaikh:2026nsi}, it was shown that for a non-relativistic particle, the operator equations of motion can be cast in the same differential form as Newton's equation of motion. This establishes a correspondence between quantum operator dynamics and classical mechanics at the level of the equations of motion. In this work, we investigate whether this correspondence extends to quantum field theory and linearized gravity. We explicitly show that the Heisenberg equations of motion for quantum field operators reproduce the corresponding classical equations of motion for a broad class of field theories. The Klein-Gordon equation, Maxwell's equations, Yang-Mills equations, and linearized Einstein equations are shown to arise at the operator level without taking the limit $\hbar\rightarrow0$. We then extend the analysis to curved spacetime and show that the quantum field operators satisfy the corresponding covariant field equations at the operator level. In the weak-field approximation, we show that the Heisenberg evolution of the metric-perturbations reproduces the linearized Einstein equations at the operator level. For a quantum particle in curved spacetime, the Heisenberg equations for position and momentum reproduce classical geodesic motion in the semiclassical limit, thereby extending the operator-level quantum-classical correspondence from fields to particle dynamics.

发表机构

• Vellore Institute of Technology（维洛尔理工学院）
• Banaras Hindu University（贝拿勒斯印度教大学）

机构由 AI 辅助整理，请以论文原文为准。

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15 pages, including 1 appendix