One non-relativistic particle coupled to a photon field

Christian Hainzl LMU-Muenchen

We investigate the ground state energy of a charged particle coupled to a photon field. First, we regard the self-energy of a “free” electron, which we describe by the Pauli-Fierz Hamiltonian. We show that, in the case of small values of the coupling constant α, the leading order term is represented by 8πα(Λ − ln[1 + Λ]).

Secondly, we treat the self-energy of a charged boson and provide a different proof for recovering the next to leading order term in α, which has already been obtained in Hainzl-Vougalter-Vugalter.

Thirdly, we estimate from above the binding energy of a charged boson in the field of a nucleus. The first order radiative correction turns out to behave like ln[1 + Λ] for large values of the ultraviolet-cutoff parameter Λ.