Nonperturbative quantum electrodynamics: The Lamb shift

1983 ◽  
Vol 13 (2) ◽  
pp. 189-194 ◽  
Author(s):  
A. O. Barut ◽  
J. Kraus
Keyword(s):  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Nonperturbative Quantum Electrodynamics

scholarly journals Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields

2021 ◽  
pp. 2150086
Author(s):  
V. P. Neznamov ◽  
V. E. Shemarulin
Keyword(s):  
Cross Sections ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Wave Functions ◽  
Self Energy ◽  
Fermion Fields ◽  
Spinor Wave

Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The final results coincide with cross-sections calculated in the standard QED. The self-energy of an electron and amplitudes of processes associated with determination of the anomalous magnetic moment of an electron and Lamb shift are calculated. These results agree with the results in the standard QED. Distinctive feature of the developed theory is the fact that only states with positive energies are present in the intermediate virtual states in the calculations of the electron self-energy, anomalous magnetic moment of an electron and Lamb shift. Besides, in equations, masses of particles and antiparticles have the opposite signs.

The Lorentz gauge in non-relativistic quantum electrodynamics

1982 ◽  
Vol 383 (1785) ◽  
pp. 485-502 ◽  
Keyword(s):  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Relativistic Quantum ◽  
Scalar Potential ◽  
Coulomb Energy ◽  
Indefinite Metric ◽  
Longitudinal Field ◽  
Lorentz Gauge ◽  
Transverse And Longitudinal Components ◽  
Relativistic Electrodynamics

It is shown how the conventional Lagrangian of non-relativistic electrodynamics leads to a theory in the Lorentz gauge where the scalar potential is treated on an equal footing with the transverse and longitudinal components of the vector potential. This requires the introduction of an indefinite metric as in the Gupta-Bleuler method. Calculations based on this approach with the use of ordinary perturbation theory for the free-space Lamb-shift of hydrogen are shown to exhibit remarkable exact cancellations between parts of the contribution arising from the scalar field and the entire contribution from the longitudinal field to order e 2 , and the result is in agreement with Bethe’s expression where only transverse photons are involved. The non-relativistic theory in the Lorentz gauge is also used to compute the order- e 2 potential on a charged particle outside a conductor where again similar exact cancellations are exhibited. The advantage of the formalism in the Lorentz gauge is emphasized in that it provides an unambiguous procedure for the evaluation of the leading Coulomb energy shifts particularly in the interaction of particles with the surfaces of active media where the Coulomb gauge may be problematical.

A precision determination of the Lamb shift in hydrogen

1979 ◽  
Vol 290 (1373) ◽  
pp. 373-404 ◽  
Keyword(s):  
Elementary Particle ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Lamb Shift ◽  
Ion Source ◽  
Interaction Region ◽  
Zero Magnetic Field ◽  
Zero Field ◽  
Hydrogen Atoms

For over 40 years, optical and microwave spectroscopists, and atomic, nuclear and elementary particle physicists have been engaged in measuring the 2 2 S ½ -2 2 P ½ energy level separation in atomic hydrogen (the Lamb shift) and attempting to predict the splitting theoretically. The discrepancies encountered have influenced the development of theoretical methods of calculation in the areas of atomic structure, quantum electrodynamics and elementary particle physics. In this paper we present the results of a precision microwave determination of the Lamb shift, using a fast atomic beam and a single microwave interaction region. The value obtained is in substantial agreement with the earlier determinations and with the recent calculation by Mohr but is in disagreement with the earlier calculation by Erickson. This disagreement is further accentuated if recent modifications to the size of the proton are included, whereas the agreement with Mohr’s calculation is not affected. The experimental method uses a 21 keV beam of metastable 2 s hydrogen atoms which are obtained by charge exchange of a proton beam extracted from a radio frequency (r.f.) ion source. The experiment is performed in essentially zero magnetic field and uses a precision transmission line interaction region to induce r.f. transitions at the Lamb shift frequency. The result for the 2 2 S ½ F = 0 to 2 2 P ½ F = 1 interval in zero field is 909.904 ± 0.020 MHz corresponding to a Lamb shift of 1057.862 ± 0.020 MHz. The paper discusses the method and the host of corrections for systematic effects which need to be applied to the line centre, many of which have not been sufficiently understood or controlled in previous experiments. The paper is introduced with a brief survey of significant landmarks in calculation and measurement of the Lamb shift and concludes with a comparison of the present theoretical and experimental positions.

Tests of quantum electrodynamics with EBIT

2008 ◽  
Vol 86 (1) ◽  
pp. 25-31 ◽  
Author(s):  
J Sapirstein ◽  
K T Cheng
Keyword(s):  
Present Status ◽  
Feynman Diagram ◽  
Quantum Electrodynamics ◽  
Nuclear Physics ◽  
Hyperfine Splitting ◽  
Lamb Shift ◽  
Nuclear Recoil ◽  
Correct Treatment ◽  
Charged Ions ◽  
Large Quantum

A Feynman-diagram-based approach to calculating the spectra of highly charged ions is described and applied to lithiumlike and sodiumlike ions. Discrepancies between calculations excluding the two-loop Lamb shift and experiment allow that shift to be determined, as the accuracy of EBIT experiments is well below the size of the effect. The present status of the theory of hyperfine splitting is described, where a large quantum electrodynamics (QED) effect is made difficult to observe because of nuclear physics uncertainties. The importance of a correct treatment of nuclear recoil at present levels of accuracy is stressed, and prospects for a full QED treatment of copperlike ions are discussed. PACS Nos.: 31.30.Jv, 32.30.Rj, 31.25.–v, 31.15.Ar

The muonic hydrogen Lamb-shift experiment

2005 ◽  
Vol 83 (4) ◽  
pp. 339-349 ◽  
Author(s):  
R Pohl ◽  
A Antognini ◽  
F D Amaro ◽  
F Biraben ◽  
J MR Cardoso ◽  
...  
Keyword(s):  
Charge Radius ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Laser System ◽  
Bound State ◽  
Muonic Hydrogen ◽  
X Rays ◽  
Large Area ◽  
Proton Charge ◽  
Proton Charge Radius

The charge radius of the proton, the simplest nucleus, is known from electron-scattering experiments only with a surprisingly low precision of about 2%. The poor knowledge of the proton charge radius restricts tests of bound-state quantum electrodynamics (QED) to the precision level of about 6 × 10–6, although the experimental data themselves (1S Lamb shift in hydrogen) have reached a precision of 2 × 10–6. The determination of the proton charge radius with an accuracy of 10–3 is the main goal of our experiment, opening a way to check bound-state QED predictions to a level of 10–7. The principle is to measure the 2S–2P energy difference in muonic hydrogen (µ–p) by infrared laser spectroscopy. The first data were taken in the second half of 2003. Muons from our unique very-low-energy muon beam are stopped at a rate of ~100 s–1 in 0.6 mbar H2 gas where the lifetime of the formed µp(2S) atoms is about 1.3 µs. An incoming muon triggers a pulsed multistage laser system that delivers ~0.2 mJ at λ ≈ 6 µm. Following the laser excitation µp(2S) → µp(2P) we observe the 1.9 keV X-rays from 2P–1S transitions using large area avalanche photodiodes. The resonance frequency, and, hence, the Lamb shift and the proton radius, is determined by measuring the intensity of these X-rays as a function of the laser wavelength. A broad range of laser frequencies was scanned in 2003 and the analysis is currently under way. PACS Nos.: 36.10.Dr, 14.20.Dh, 42.62.Fi

scholarly journals Some recent advances in bound-state quantum electrodynamics

2005 ◽  
Vol 83 (4) ◽  
pp. 375-386 ◽  
Author(s):  
U D Jentschura ◽  
J Evers
Keyword(s):  
Effective Field Theories ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Recent Progress ◽  
Bound State ◽  
Effective Field ◽  
Field Theories ◽  
Nonrelativistic Quantum ◽  
Self Energy ◽  
Bound Electron

We discuss recent progress in various problems related to bound-state quantum electrodynamics: the bound-electron g factor, two-loop self-energy corrections, and the laser-dressed Lamb shift. The progress relies on various advances in the bound-state formalism, including ideas inspired by effective field theories such as nonrelativistic quantum electrodynamics. Radiative corrections in dynamical processes represent a promising field for further investigations. PACS Nos.: 31.15.–p, 12.20.Ds

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