01-478 Christian Hainzl

One non-relativistic particle coupled to a photon field (47K, LaTeX2e) Dec 19, 01

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Abstract. 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 $\alpha$, the leading order term is represented by $8\pi \alpha (\Lambda - \ln[1 + \Lambda])$. Secondly, we treat the self-energy of a charged boson and provide a different proof for recovering the next to leading order term in $\alpha$, which has already been obtained in a previous paper. 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 $\ln[1+\Lambda]$ for large values of the ultraviolet-cutoff parameter $\Lambda$.

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