Quantum electrodynamics perturbation theory

This is due to the comparative weakness of the electromagnetic interaction, the theory of which contains a small dimensionless parameter (fine structure constant), by the powers of which the corresponding quantities can be expanded. The electron transition probability of the radiation of one photon, characterized by a definite value of angular momentum, in the first order of quantum-electrodynamical perturbation theory mdy be described as follows [53] (a.u.) ... 

What has been presented here is a semiclassical theory of TJ 1) quantum electrodynamics. Here the electromagnetic field is treated in a purely classical manner, but where the electromagnetic potential has been normalized to include one photon per some unit volume. Here the absorption and emission of a photon is treated in a purely perturbative manner. Further, the field normalization is done so that each unit volume contains the equivalent of n photons and that the energy is computed accordingly. However, this is not a complete theory, for it is known that the transition probability is proportional to n + 1. So the semiclassical theory is only appropriate when the number of photons is comparatively large. 

It now remains to expand the operators in (3.235) using the definitions given in (3.230) but before we do so we must draw attention to a difficulty with (3.235). The final term, containing the operator (00)2 is not obtained if a more sophisticated treatment starting from the Bethe Salpeter equation is used. The reader will recall our earlier comment that the interaction term in the Breit Hamiltonian is acceptable provided it is treated by first-order perturbation theory. Rather than launch into quantum electrodynamics at this stage, we shall proceed to develop (3.235) but will omit the (00)2 term without further comment. 

Here, what said in Section 4.2 about time-dependent perturbations is worth recalling, trying to give a more detailed analysis. The best approach to treat problems characterized by the presence of a P(t) function is provided by the quantum electrodynamics theories, where P is described in terms of an expansion over normal modes of the dielectric polarization. This model can be simplified by considering only two terms, often called the fast and the slow contribution to P (the Pekar separation introduced in eq.(18) of Section 4.2) ... 

This paper is dedicated to Professor Ingvar Lindgren in connection with his 65th anniversary in view of his many outstanding contributions to physics and particularly to the development of perturbation theory and its applications to the non-relativistc theory of atomic and molecular systems and in some cases also to relativistic corrections by means of quantum electrodynamics. 

It turns out that in an appropriate formulation of perturbation theory only even orders of c or Zc appear. We nevertheless count the orders of PT in terms of c , such that the leading corrections to the energy are c E i,c Ei etc. Some authors use an alternative counting, replacing our E2, E4 etc. by El, E etc. This reflects the fact that our E2 is obtained by formally applying first-order PT. We prefer the counting in powers of c for various reasons. In some situations odd orders of c" arise explicitly, and would require fractional orders in c otherwise. Quantum electrodynamics (QED) corrections contain odd orders in even for the energy. 

We start this chapter with a discussion of the non-relativistic limit (nrl) of relativistic quantum theory (section 2). The Levy-Leblond equation will play a central role. We also discuss the nrl of electrodynamics and study how properties differ at their nrl from the respective results of standard non-relativistic quantum theory. We then present (section 3) the Foldy-Wouthuysen (FW) transformation, which still deserves some interest, although it is obsolete as a starting point for a perturbation theory of relativistic corrections. In this context we discuss the operator X, which relates the lower to the upper component of a Dirac bispinor, and give its perturbation expansion. The presentation of direct perturbation theory (DPT) is the central part of this chapter (section 4). We discuss the... 

For further details the reader is referred to, e.g., a review article by Kutzel-nigg [67]. The Gaunt- and Breit-interaction is often not treated variationally but rather by first-order perturbation theory after a variational treatment of the Dirac-Coulomb-Hamiltonian. The contribution of higher-order corrections such as the vaccuum polarization or self-energy of the electron can be derived from quantum electrodynamics (QED), but are usually neglected due to their negligible impact on chemical properties. 

Quantum Electrodynamics and Many-body Perturbation Theory. - In his... 

Investigation of the connection between the Many-Body Perturbation Theory (MBPT) approach and the Furry representation of Quantum Electrodynamics (QED) has been shown to allow a precise definition of QED effects.82 Every MBPT diagram has a corresponding Feynman diagram, but there are Feynman diagrams that have no MBPT counterpart. 

An overview of the salient features of the relativistic many-body perturbation theory is given here concentrating on those features which differ from the familiar non-relativistic formulation and to its relation with quantum electrodynamics. Three aspects of the relativistic many-body perturbation theory are considered in more detail below the representation of the Dirac spectrum in the algebraic approximation is discussed the non-additivity of relativistic and electron correlation effects is considered and the use of the Dirac-Hartree-Fock-Coulomb-Breit reference Hamiltonian demonstrated effects which go beyond the no virtual pair approximation and the contribution made by the negative energy states are discussed. 

We have presented a relativistically covariant many-body perturbation procedure, based upon the CEO and the GO. This represents a unification of the many-body perturbation theory and quantum electrodynamics. Applied to all orders, the procedure leads in the equal-time approximation to the BSE in the effective-potential form. By relaxing this restriction, the procedure is consistent with the full BSE. The new procedure will be of importance in cases where QED effects beyond first order in combination with high-order electron correlation are significant. 

This paper reviews progress in the application of atomic isotope shift measurements, together with high precision atomic theory, to the determination of nuclear radii from the nuclear volume effect. The theory involves obtaining essentially exact solutions to the nonrelativistic three- and four-body problems for helium and lithium by variational methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. The results are applied to the calculation of isotope shifts for the short-... 

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