Non analyticity of the ground state energy of the Hamiltonian for Hydrogen atom in nonrelativistic QED

Jean-Marie Barbaroux (1, 2) , Semjon Vugalter (3)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332
3 Mathematik, Universitaet Muenchen

We derive the ground state energy up to the fourth order in the fine structure constant for the translation invariant Pauli-Fierz Hamiltonian for a spinless electron coupled to the quantized radiation field. As a consequence, we obtain the non-analyticity of the ground state energy of the Pauli-Fierz operator for a single particle in the Coulomb field of a nucleus.

Domaines: Théorie spectrale [math.SP]; Physique Quantique [quant-ph]

Jean-Marie Barbaroux, Semjon Vugalter. Non analyticity of the ground state energy of the Hamiltonian for Hydrogen atom in nonrelativistic QED. Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.474004. ⟨10.1088/1751-8113/43/47/474004⟩. ⟨hal-00488167⟩