Nonrelativistic Quantum Electrodynamics Research Articles

Eigenfunctions of the Vector-Potential Operator of the Electromagnetic Field and Semiclassical Electrodynamics

A complete orthonomnal set of eigenfunctions of the vector-potential operator is introduced. It is shown that the semiclassical approximation is naturally determined in the basis of the functions introduced. The extraction of the semiclassical approximation from nonrelativistic quantum electrodynamics allows the determination of the limits of applicability of the semiclassical approach. It is shown that the semiclassical approximation is inapplicable at sufficiently large photon densities. The advantages of using our set of eigenfunctions for the description of the interaction of a strong quantized field with a quantum system are discussed. (auth)

Comments on a Proposed Quantization of Interacting Fields

The meaning of a recently proposed formalism for quantization of interacting fields is discussed by studying the consequences of the time-dependent unitary transformation which is essential for this approach. It turns out that non-relativistic quantum electrodynamics in dipole approximation may serve as a useful, although rather singular, example for this method. In the relativistic case a different point of view is suggested in order to avoid inconsistent interpretation. It is further possible to give arguments for a reasonable choice of the unitary transformation concerned

Electrodynamics of direct interparticle action: II. Relativistic treatment of radiative processes

This paper is a sequel to an earlier paper that described nonrelativistic quantum electrodynamics in terms of the time symmetric theory of direct interparticle action. The restriction to a nonrelativistic treatment is removed in the present paper. The path integral approach to quantum mechanics is extended to include relativistic particles with spin as a preliminary to achieving this end. The response of the Universe can be obtained in two ways, by an extension of the method of the previous paper or by using a general condition analogous to the general condition, Σ particles[ F ret − F adv] = 0, of Wheeler and Feynman. The second method is used in the present paper since it avoids the need to calculate the detailed properties of the absorber. The rules of quantum electrodynamics in the form stated by Feynman are derived, thereby showing that all the practical results of the usual theory of quantum electrodynamics can also be obtained from the direct particle theory. Radiation corrections are discussed. The direct particle theory throws some light on the processes of renormalization. The point of view that both mass and charge should be finite before as well as after renormalization is partially developed.

Quantization of interacting fields

It is shown that the canonical quantization scheme does not lead to a unique formulation of quantum field theory because of the freedom to make time dependent unitary transformations involving a (classical) Boson field, before quantization. As examples, alternative formulations of both non-relativistic and relativistic quantum electrodynamics, in agreement with the correspondence principle, are given. These yield an S-matrix which is free of all divergences, at least to the second order.

Coulomb gauge in non-relativistic quantum electro-dynamics and the shape of spectral lines

An examination is made of the Green dyadic for the propagation functions of non-relativistic quantum electrodynamics in the Coulomb gauge div A = 0. The existence of false precursors is shown to be associated with singularities at the origin in certain momentum space representations of the propagators and this allows a prescription to be given to eliminate such precursors. This prescription is proved equivalent to an exact consideration of the near fields associated with quantum transitions. The analogous treatment for the state vectors in decaying systems is carried through and is applied in detail to the problems of the shape of natural spectral lines and the transition rate for stimulated emission. It is shown that the expected line shape for the Lamb 1057 Mc/s line in hydrogen is Lorentzian within the context of Lamb’s experiments—intensity against Zeeman splitting energy. This is in contradiction to the predictions of Arnous and Heitler. The distribution in k (circular frequency) for a natural line, on the other hand, has a factor k <super>a</super> times the resonant denominator. The definitive position between the conflicting transition rates in the literature is given. The relationship of the calculations to a gauge-independent Hamiltonian, considered in the paper, is investigated in detail. This Hamiltonian, transformed canonically from the conventional one, is shown to be valid for internal, dynamical, quantized electromagnetic fields; its analogue in the case of external applied fields being well known. It is demonstrated that the transformation eliminates many of the difficulties associated with the false near fields and that it also allows certain radiative effects, where the atom acts as a whole, to be computed in a straightforward manner.

Mass renormalization and energy level shift in non-relativistic QED

Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge Z and in presence of the quantized radiation field. � =