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Existence of ground states of hydrogenlike atoms in relativistic quantum electrodynamics I: The semirelativistic PauliFierz operator
 Rev. Math. Phys
, 2011
"... Abstract. We consider a hydrogenlike atom in a quantized electromagnetic field which is modeled by means of a nopair operator acting in the positive spectral subspace of the free Dirac operator minimally coupled to the quantized vector potential. We prove that the infimum of the spectrum of the no ..."
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Abstract. We consider a hydrogenlike atom in a quantized electromagnetic field which is modeled by means of a nopair operator acting in the positive spectral subspace of the free Dirac operator minimally coupled to the quantized vector potential. We prove that the infimum of the spectrum of the nopair operator is an evenly degenerate eigenvalue. In particular, we show that the bottom of its spectrum is strictly less than its ionization threshold. These results hold true, for arbitrary values of the finestructure constant and the ultraviolet cutoff and for all Coulomb coupling constants less than the critical one of the BrownRavenhall model, 2/(2/π+π/2). For Coulomb coupling constants larger than the critical one, we show that the quadratic form of the nopair operator is unbounded below. Along the way wediscussthedomainsandoperatorcoresofthesemirelativisticPauliFierz and nopair operators, for Coulomb coupling constants less than or equal to the critical ones. 1.
Renormalization Group and Problem of Radiation
, 2011
"... The standard model of nonrelativistic quantum electrodynamics describes nonrelativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this model, we review basic notions, results and techniques in the theory of radiation. We describe the key te ..."
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Cited by 1 (0 self)
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The standard model of nonrelativistic quantum electrodynamics describes nonrelativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this model, we review basic notions, results and techniques in the theory of radiation. We describe the key technique in this area the spectral renormalization group. Our review is based on joint works with Volker Bach
Renormalization Group and Problem of Radiation, Les Houches, August 2010
, 2011
"... The standard model of nonrelativistic quantum electrodynamics describes nonrelativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this model, we review basic notions, results and techniques in the theory of radiation. We describe the key te ..."
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The standard model of nonrelativistic quantum electrodynamics describes nonrelativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this model, we review basic notions, results and techniques in the theory of radiation. We describe the key technique in this area the spectral renormalization group. Our review is based on joint works with Volker Bach