It is physically expected that plane-wave configurations of the electron in QED induce disjoint representations of the algebra of the electromagnetic fields. This phenomenon of velocity superselection, which is one aspect of the infrared problem, is mathematically well established in non-relativistic (Pauli–Fierz type) models of QED. We show that velocity superselection can be resolved in such models by restricting the electron states to the subalgebra of the fields localized in the future lightcone. This actually follows from a more general statement about equivalence of GNS representations for coherent states of the algebra of the future lightcone in free electromagnetism. Our analysis turns out to be meaningful in the non-relativistic setting and provides evidence in favour of the Buchholz–Roberts approach to infrared problems.

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非相对论QED的光速锥约束固化速度超选择

物理上可以预料，QED中电子的平面波配置会引起电磁场代数的不相交表示。这种速度超选择现象是红外问题的一个方面，在QED的非相对论（Pauli–Fierz型）模型中在数学上已经很好地建立了。我们表明，通过将电子状态限制在未来光锥中局部场的子代数，可以在这种模型中解决速度超选择问题。实际上，这是根据关于自由电磁中未来光锥代数的相干状态的GNS表示的等效性的更笼统的陈述得出的。我们的分析在非相对论的背景下被证明是有意义的，并提供了支持布赫霍尔茨-罗伯茨方法解决红外问题的证据。