非零纽结的相干态
Coherent States of Non-Null Torus Knots
AI总结：
本文研究非零纽结经典解对应的量子电磁场相干态，推导位移算符并验证相干态性质，计算场期望值、能量密度等可观测量，建立真空拓扑电磁系统的量子-经典对应。
摘要：
我们构建了量子化电磁场的相干态，对应真空中的经典非零扭结解。通过经典场与相干态幅值的一般关系推导位移算符，并通过直接计算验证相干态定义性质。我们确定了模型的可观测量：场期望值、能量密度、坡印廷向量、手征度、光子数、四分量不确定性和相关函数，并以整数参数(n,m,l,s)计算其在扭结相干态中的期望值。以霍夫离子相干态为例，这些结果建立了此类真空拓扑电磁系统的量子-经典对应。
英文摘要：
We construct coherent states for the quantized electromagnetic field that correspond to the classical non-null torus knot solutions of Maxwell's equations in vacuum. We derive the displacement operators from the general relation between classical fields and coherent state amplitudes and verify the defining properties of coherent states through direct computation. We determine the observables of the model: field expectation values, energy density, Poynting vector, helicity, photon number, quadrature uncertainties, and correlation functions, and calculate their expectation values in the knotted coherent states in terms of the integer parameters $(n,m,l,s)$ of the classical solutions. As an example, we particularize the construction in the case of the Hopfion coherent state. These results establish the quantum-classical correspondence for this type of vacuum topological electromagnetic systems.
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