Thursday, February 16, 2012

1202.3189 (Volker Bach et al.)

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

Volker Bach, Thomas Chen, Jeremy Faupin, Juerg Froehlich, Israel Michael Sigal
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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