Interaction with an external field in quantum electrodynamics

Russian Physics Journal -     

Maxwell electrodynamics subjected to quantum vacuum fluctuations

The propagation of electromagnetic waves in the vacuum is considered taking into account quantum fluctuations in the limits of Maxwell-Langevin (ML) equations. For a model of “white noise” fluctuations, using ML equations, a second order partial differential equation is found which describes the quantum distribution of virtual particles in vacuum. It is proved that in order to satisfy observed facts, the Lamb Shift etc, the virtual particles should be quantized in unperturbed vacuum. It is shown that the quantized virtual particles in toto (approximately 86 percent) are condensed on the “ground state” energy level. It is proved that the extension of Maxwell electrodynamics with inclusion of the vacuum quantum field fluctuations may be constructed on a 6D space-time continuum with a 2D compactified subspace. Their influence on the refraction indexes of vacuum is studied.     

Chaotic Rabi vacuum oscillations in cavity quantum electrodynamics

It is shown in numerical simulations with two-level atoms moving through a single-mode high-Q cavity that spontaneous emission of a new type — chaotic Rabi vacuum oscillations — arises in the strong atom-field coupling regime. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 11, 801–806 (10 June 1997)     

The quantum vacuum at the foundations of classical electrodynamics

In the classical theory of electromagnetism, the permittivity ε ₀ and the permeability μ ₀ of free space are constants whose magnitudes do not seem to possess any deeper physical meaning. By replacing the free space of classical physics with the quantum notion of the vacuum, we speculate that the values of the aforementioned constants could arise from the polarization and magnetization of virtual pairs in vacuum. A classical dispersion model with parameters determined by quantum and particle physics is employed to estimate their values. We find the correct orders of magnitude. Additionally, our simple assumptions yield an independent estimate for the number of charged elementary particles based on the known values of ε ₀ and μ ₀ and for the volume of a virtual pair. Such an interpretation would provide an intriguing connection between the celebrated theory of classical electromagnetism and the quantum theory in the weak-field limit.     

Canonical dimensions for the electromagnetic field and current in quantum electrodynamics

It is suggested that the Gell-Mann Low function vanishes for a fixed (large) value of the unrenormalized coupling constant.     

Two-dimensional quantum electrodynamics as a model in the constructive quantum field theory

We investigate a transformation of two-dimensional quantum electrodynamics ((QED)₂)-type models into sine-Gordon models in the constructive method.     

Experimental tests of quantum electrodynamics in weak field

This paper resumes the most precise tests of QED. We mainly describe the recent measurements of the Lamb shifts in hydrogen, deuterium and helium. The new optical frequency measurements of the 1s–2s and 2s–8s transitions in hydrogen and deuterium give now the most precise determination of the Rydberg constant and of the Lamb shifts of the 1s and 2s levels. The accurate measurement of the 2³S₁ Lamb shift in helium is also presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

On refractive processes in strong laser field quantum electrodynamics

Refractive processes in strong-field QED are pure quantum processes, which involve only external photons and the background electromagnetic field. We show analytically that such processes occurring in a plane-wave field and involving external real photons are all characterized by a surprisingly modest net exchange of energy and momentum with the laser field, corresponding to a few laser photons, even in the limit of ultra-relativistic laser intensities. We obtain this result by a direct calculation of the transition matrix element of an arbitrary refractive QED process and accounting exactly for the background plane-wave field. A simple physical explanation of this modest net exchange of laser photons is provided, based on the fact that the laser field couples with the external photons only indirectly through virtual electron–positron pairs. For stronger and stronger laser fields, the pairs cover a shorter and shorter distance before they annihilate again, such that the laser can transfer to them an energy corresponding to only a few photons. These results can be relevant for the future experiments aiming to test strong-field QED at present and next-generation facilities.     

Nonresonant quantum electrodynamics processes in a pulsed laser field

This review contains theoretical study of nonresonant quantum electrodynamics processes of the first and second orders in the fine-structure constant in a pulsed laser field. The approximation is examined when the pulse width is considerably greater than the characteristic time of wave oscillations. It was demonstrated that for nonrelativistic particle energy the differential cross section of a process in a pulsed light fields may considerably difference from the corresponding cross section in an absence of a laser field. Results obtained may be experimentally verified by the scientific facilities at the SLAC National Accelerator Laboratory and FAIR (Facility for Antiproton and Ion Research, Darmstadt, Germany) project.     

On vacuum instability in quantum field theory

The imaginary part of the phase of the vacuum to vacuum transition amplitude is computed for a class of diagrams involving renormalons. It is found that for these particular diagrams the imaginary part of the phase is finite. We suggest that in general the divergences are at most logarithmic and that they are therefore hopefully renormalizable. In asymptotically free theories this implies that the vacuum is unstable.     

The Furry picture in scalar quantum electrodynamics with a strong pair-producing external field

The Furry picture is obtained in the case of scalar quantum electrodynamics with a strong pair-producing external field. Rules are derived for calculating the matrix elements.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 37–42, June, 1980.     

Towards hybrid circuit quantum electrodynamics with quantum dots

Cavity quantum electrodynamics allows one to study the interaction between light and matter at the most elementary level. The methods developed in this field have taught us how to probe and manipulate individual quantum systems like atoms and superconducting quantum bits with an exquisite accuracy. There is now a strong effort to extend further these methods to other quantum systems, and in particular hybrid quantum dot circuits. This could turn out to be instrumental for a noninvasive study of quantum dot circuits and a realization of scalable spin quantum bit architectures. It could also provide an interesting platform for quantum simulation of simple fermion–boson condensed matter systems. In this short review, we discuss the experimental state of the art for hybrid circuit quantum electrodynamics with quantum dots, and we present a simple theoretical modeling of experiments.     

Equations for the Green functions in quantum electrodynamics

Using the Freese-Matthews-Salam equations for chronological products of field operators, equations are written for Green functions of many electrons and photons. It is shown that in order to find any single Green function an infinite recursive system of these equations has to be solved. After adding terms containing the external electric current and external electromagnetic potential to the Lagrangian, this system is reduced to one equation containing functional derivatives of higher orders. It is shown that all relations and equations become much simpler when the definition of the Green function is appropriately changed.On leave from the Physical Institute of the Czechoslovak Academy of Sciences, Prague, Czechoslovakia.