量子点电荷与准经典电磁场的相互作用
Quantum Point Charges Interacting with Quasi-classical Electromagnetic Fields
AI总结：
本文研究准经典区域中量子点粒子与量子化电磁场的耦合，通过迹离场自由度得到含场状态信息的有效 Schrödinger 算子，并证明无紫外截断时模型仍适定。
摘要：
我们研究描述量子粒子系统在准经典区域（即场的状态表现出较大的平均激发数时）与量子化（电磁）场相互作用的有效模型。一旦在因子化状态上迹去场的自由度，粒子系统的约化动力学就由一个记录场状态的有效 Schrödinger 算子描述。我们证明，在对后者作适当假设的条件下，即使粒子是点状的，即对其与量子场的相互作用不施加紫外截断，此类有效模型仍是适定的。
英文摘要：
We study effective models describing systems of quantum particles interacting with quantized (electromagnetic) fields in the quasi-classical regime, i.e., when the field's state shows a large average number of excitations. Once the field's degrees of freedom are traced out on factorized states, the reduced dynamics of the particles' system is described by an effective Schrödinger operator keeping track of the field's state. We prove that, under suitable assumptions on the latter, such effective models are well-posed even if the particles are point-like, that is no ultraviolet cut-off is imposed on the interaction with quantum fields.
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