Abstract
The time evolution of the Lamb shift that accompanies the real photon emission is studied for the first time (to our knowledge). The investigation of the explicit time dependence of the Lamb shift becomes possible because the self-energy of the free electron, which is divergent, is subtracted from the Hamiltonian after a unitary transformation. The Lamb shift can then be separated into two parts: one is the time-independent shift due to the virtual photon exchange, and the other is the time-dependent shift due to the real photon emission. The time evolution depends on the nature of the coupling spectrum of the reservoir.
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