Effective dynamics of an electron coupled to an external potential in non-relativistic QED

Details Effective dynamics of an electron coupled to an external potential in non-relativistic QED Effective dynamics of an electron coupled to an external potential in non-relativistic QED

2012-02-15

arxiv.org/abs/1202.3189v1

Physics

Mathematical Physics

24 pages, AMS Latex

Scientific paper

In the framework of non-relativistic QED, we establish the relationship between the renormalized mass of the electron due to its interaction with the quantized electromagnetic field, and the kinematic mass appearing in its response to a slowly varying external force. Specifically, we study the dynamics of an electron in a slowly varying external potential and with slowly varying initial conditions and prove that, for a long time, it is accurately described by the effective dynamics of a Schr\"odinger electron in the same external potential and for the same initial data, with a kinetic energy operator determined by the renormalized dispersion law of the translation-invariant QED model.

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