Quantum electrodynamics of confined nonrelativistic particles
type: Item
instance of: scholarly article
title: Quantum electrodynamics of confined nonrelativistic particles
zbMATH Open document ID: 0923.47040
author: Volker Bach
author: Jürg Fröhlich
author: I. M. Sigal
published in: Advances in Mathematics
publication date: 1999-10-31T00:00:00Z
review text: The model treated is a modified standard model of nonrelativistic quantum electrodynamics where the coupling functions are assumed to have a better behaviour for large distances. The results are the following: The system has a ground state. It is exponentially localized in the particle coordinates. The excited states become unstable. The spectrum is purely absolutely continuous outside certain neighbourhoods of thresholds. Resonances exist. They are related to poles of meromorphically continued resolvent matrix elements. Their real part is given by Bethe's formula, their imaginary part is determined by Fermi's golden rule. For the hydrogen atom the Lamb shifts are quite accurate.
reviewed by: Michael Demuth
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81V10
zbMATH DE Number: 1215513
zbMATH Keywords: resonances exist
zbMATH Keywords: nonrelativistic quantum electrodynamics
zbMATH Keywords: ground state
zbMATH Keywords: exponentially localized
zbMATH Keywords: excited states
zbMATH Keywords: Bethe's formula
zbMATH Keywords: Fermi's golden rule
zbMATH Keywords: hydrogen atom
zbMATH Keywords: Lamb shifts
MaRDI profile type: Publication
full work available at URL: aima.1998.1734
OpenAlex ID: W2037748774
cites work: On a model of a harmonic oscillator coupled to a quantized, massless, scalar field. I
cites work: Self-adjointness and spectrum of Hamiltonians in nonrelativistic quantum electrodynamics
cites work: On the existence and uniqueness of ground states of a generalized spin-boson model
cites work: Mathematical theory of nonrelativistic matter and radiation
cites work: Renormalization group analysis of spectral problems in quantum field theory
cites work: Q3264049
cites work: The Electromagnetic Shift of Energy Levels
cites work: Q3756011
cites work: A new proof of the Mourre estimate
cites work: Q3017967
cites work: ASYMPTOTIC COMPLETENESS FOR THE SPIN-BOSON MODEL WITH A PARTICLE NUMBER CUTOFF
cites work: The \(\lambda (\varphi^ 4)_ 2\) quantum field theory without cutoffs. II: The field operators and the approximate vacuum
cites work: RADIATIVE DECAY: NONPERTURBATIVE APPROACHES
cites work: Q4837798
cites work: Q3756006
cites work: Resonances, metastable states and exponential decay laws in perturbation theory
cites work: Q4836260
cites work: Q4854380
cites work: On a model for quantum friction. III: Ergodic properties of the spin -- boson system
cites work: Spectral theory of thermal relaxation
cites work: Smooth operators and commutators
cites work: Absolute Continuity of Hamiltonian Operators with Repulsive Potential
cites work: Absence of singular continuous spectrum for certain self-adjoint operators
cites work: Q3725227
cites work: Spectral analysis of N-body Schrödinger operators
cites work: Q5528957
cites work: Q4185363
cites work: Q3684681
cites work: Stark effect in multielectron systems: Non-existence of bound states
cites work: Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory
cites work: Ground state(s) of the spin-boson Hamiltonian
cites work: Q5607484
DOI: 10.1006/AIMA.1998.1734
description: scientific article; zbMATH DE number 1215513