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Time-Dependent Perturbation Theory with Application to Atomic Systems

Chapter in book
Authors Ingvar Lindgren
Published in Advances in Quantum Chemistry - Löwdin Volume. Chapter 5
Pages 83-105
ISBN 978-0-12-809988-9
Publisher Elsevier
Publication year 2017
Published at Department of Physics (GU)
Pages 83-105
Language en
Keywords many-particle systems, quantum-theory, body problem, connection, expansion, equation, state
Subject categories Quantum chemistry


A new form of time-dependent perturbation theory has been developed based upon the covariant-evolution operator (CEO), previously introduced by us. This has made it possible to combine time-dependent perturbations, like the quantum-electrodynamical (QED) perturbations, with time-independent interactions, like the Coulomb interaction (electron correlation) in a single perturbation expansion. For the first time quantum-electrodynamical perturbations can then be combined with electron correlation beyond second order. The experimental accuracy is inmany cases so high that these effects have become significant. A numerical scheme has been developed where first-order QED effects are combined with the electron correlation and applied to highly charged helium-like ions. This scheme contains the dominating part of the higher-order QED effects and has been applied to highly charged helium-like ions, for which effects beyond second order (two-photon effects) have for the first time been evaluated. The calculations have been performed using Feynman as well as Coulomb gauge. In evaluating effects beyond second order involving radiative QED it was necessary to employ the Coulomb gauge.

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