J.E. Avron and A. Elgart
An Adiabatic Theorem with Soft Photons
(44K, LATeX 2e)
ABSTRACT. The adiabatic theorem of Quantum Mechanics disregards the soft
photons of QED. Why, then, is it so successful? To understand the role of soft
photons we prove an adiabatic theorem for the ground state of a simple model
Hamiltonians that allows soft photons. We show that for weak electron-photon
coupling, the adiabatic time scale is close to the
time scale in a theory without the quantized radiation field
up to a Lamb shift. The inclusion of
photons also leads to a logarithmic correction in three dimensions coming from
an infrared singularity characteristic of QED.