Non-Relativistic Matter and Quantized Radiation

Griesemer, Marcel

doi:10.1007/3-540-32579-4_5

Cited by 8 publications

(9 citation statements)

References 54 publications

(169 reference statements)

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“…For justifications of this model see [8,11]. A (pure) state of system of N spinless electrons and transversal photons is described by a vector in the Hilbert space…”

Section: Non-relativistic Qed In Dipole-approximationmentioning

confidence: 99%

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

Griesemer

Hasler

2009

Ann. Henri Poincaré

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Abstract.For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of α 3/2 , α being the fine structure constant. A suitably chosen ground state vector depends analytically on α 3/2 and it is twice continuously differentiable with respect to the nuclear coordinates.

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“…For justifications of this model see [8,11]. A (pure) state of system of N spinless electrons and transversal photons is described by a vector in the Hilbert space…”

Section: Non-relativistic Qed In Dipole-approximationmentioning

confidence: 99%

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

Griesemer

Hasler

2009

Ann. Henri Poincaré

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“…First we are faced with the lack of smoothness of the ǫ µ (k)'s which define vector fields on spheres |k| =cst (see [26,18]). It suffices to consider one example.…”

Section: Proofmentioning

confidence: 99%

The dressed mobile atoms and ions

Amour

Grébert

Guillot

2006

Journal de Mathématiques Pures et Appliquées

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We consider free atoms and ions in R 3 interacting with the quantized electromagnetic field. Because of the translation invariance we consider the reduced hamiltonian associated with the total momentum. After introducing an ultraviolet cutoff we prove that the reduced hamiltonian for atoms has a ground state if the coupling constant and the total momentum are sufficiently small. In the case of ions an extra infrared regularization is needed. We also consider the case of the hydrogen atom in a constant magnetic field. Finally we determine the absolutely continuous spectrum of the reduced hamiltonian.

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“…Actually it follows by mimicking [20,21,16] (see also [34]) and, here, we only give a sketch of the proof. In this appendix we are faced with the lack of smoothness of the ǫ µ (k)'s which define vector fields on spheres |k| =cst (see [33,23]). It suffices to consider one example.…”

Section: A Exitences Of a Ground State For The Hamiltonian With Inframentioning

confidence: 99%

The dressed nonrelativistic electron in a magnetic field

Amour

Grébert

Guillot

2006

Math Methods in App Sciences

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We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the x3-axis and with a quantized electromagnetic field. When the interaction between the electron and photons is turned off, the electronic system is assumed to have a ground state of finite multiplicity. Because of the translation invariance along the x3-axis, we consider the reduced Hamiltonian associated with the total momentum along the x3-axis and, after introducing an ultraviolet cutoff and an infrared regularization, we prove that the reduced Hamiltonian has a ground state if the coupling constant and the total momentum along the x3-axis are sufficiently small. We determine the absolutely continuous spectrum of the reduced Hamiltonian and, when the ground state is simple, we prove that the renormalized mass of the dressed electron is greater than or equal to its bare one. We then deduce that the anomalous magnetic moment of the dressed electron is non negative.

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Non-Relativistic Matter and Quantized Radiation

Cited by 8 publications

References 54 publications

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

The dressed mobile atoms and ions

The dressed nonrelativistic electron in a magnetic field

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