Convergent expansions in non-relativistic QED: Analyticity of the ground state

Details Convergent expansions in non-relativistic QED: Analyticity of the ground state Convergent expansions in non-relativistic QED: Analyticity of the ground state

2010-05-19

arxiv.org/abs/1005.3522v2

Physics

Mathematical Physics

37 pages

Scientific paper

We consider the ground state of an atom in the framework of non-relativistic qed. We show that the ground state as well as the ground state energy are analytic functions of the coupling constant which couples to the vector potential, under the assumption that the atomic Hamiltonian has a non-degenerate ground state. Moreover, we show that the corresponding expansion coefficients are precisely the coefficients of the associated Raleigh-Schroedinger series. As a corollary we obtain that in a scaling limit where the ultraviolet cutoff is of the order of the Rydberg energy the ground state and the ground state energy have convergent power series expansions in the fine structure constant $\alpha$, with $\alpha$ dependent coefficients which are finite for $\alpha \geq 0$.

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