Lamb shift quantum electrodynamics

This experimental development was matched by rapid theoretical progress, and the comparison and interplay between theory and experiment has been important in the field of metrology, leading to higher precision in the determination of the fundamental constants. We feel that now is a good time to review modern bound state theory. The theory of hydrogenic bound states is widely described in the literature. The basics of nonrelativistic theory are contained in any textbook on quantum mechanics, and the relativistic Dirac equation and the Lamb shift are discussed in any textbook on quantum electrodynamics and quantum field theory. An excellent source for the early results is the classic book by Bethe and Salpeter [6]. A number of excellent reviews contain more recent theoretical results, and a representative, but far from exhaustive, list of these reviews includes [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. 

In this section we discuss the nonrelativistic 0(3) b quantum electrodynamics. This discussion covers the basic physics of f/(l) electrodynamics and leads into a discussion of nonrelativistic 0(3)h quantum electrodynamics. This discussion will introduce the quantum picture of the interaction between a fermion and the electromagnetic field with the magnetic field. Here it is demonstrated that the existence of the field implies photon-photon interactions. In nonrelativistic quantum electrodynamics this leads to nonlinear wave equations. Some presentation is given on relativistic quantum electrodynamics and the occurrence of Feynman diagrams that emerge from the B are demonstrated to lead to new subtle corrections. Numerical results with the interaction of a fermion, identical in form to a 2-state atom, with photons in a cavity are discussed. This concludes with a demonstration of the Lamb shift and renormalizability. 

In 1947 Lamb and Retherford observed the 22-p3/2 — 225 1/2 transition using microwave techniques and found it to have a wavenumber 0.0354 cm 1 less than predicted by Dirac. The corresponding shift of the energy level, known as the Lamb shift, is shown in Figure 7.8 the 22.P,, 2 level is not shifted. Later, Lamb and Retherford observed the 22S1/2 — 22P1/2 transition directly with a wavenumber of 0.0354 cm-1. Quantum electrodynamics is the name given to the modified Dirac theory which accounts for the Lamb shift. 

By comparison of one quarter of the IS1 — 25 transition frequency with the 25 — 45 and 25 — 4D transition frequency, the main energy contributions described by the simple Rydberg formula are eliminated. The remaining difference frequency (about 5 GHz) is determined by well known relativistic contributions, the hyperfine interaction, and a combination of Lamb shifts. Since quantum electrodynamic contributions scale roughly as 1/n3 with the principal quantum number, the Lamb shift of the 15 level is the largest. 

The discovery of the 25 — 2P Lamb shift has led to the development of the theory of quantum electrodynamics. Today, radio frequency measurements of this splitting have reached the uncertainty limits imposed by the 100 MHz natural linewidth of the 2P state. The considerably sharper optical two-photon resonances used in optical experiments leave significant room for future improvements. 

Abstract. We report progress towards making a precise measurement of the 2S Lamb shift in singly-ionised helium by spectroscopy of the 2S-3S transition. The motivation for the experiment is discussed with reference to recent developments in the theory of quantum electrodynamics (QED) and a description of the apparatus and techniques used is given. 

The paper that reported these results ended with the recognition that there was a problem Whether the failure of theory and experiment to agree is because of some unknown factor in the theory of the hydrogen atom or simply an error in the estimate of one of the natural constants, such as [the fine structure constant], only further experiment can decide. This was the result that Rabi conveyed to the physicists at Shelter Island. Rabi s reputation as an experimentalist brought credibility to the measured results and issued a challenge to the theorists. As with the Lamb shift, it was quantum electrodynamics that was brought to bear on... 

At that time, in the 1950s, there was a problem whereby the calculations from quantum electrodynamics for the Lamb shift, 2 Si/2 — 2P /2 in the states of hydrogen, were not in exact agreement with the measurements. Thus it occurred to me that a small violation of parity symmetry in the electromagnetic interaction might be responsible for this discrepancy. 

The Lamb experiment was the primary stimulus leading to the development of a non-relativistic Quantum Electrodynamics (QED) by Kramers, Bethe, Schwinger, Weisskopf and others. The Lamb shift was interpreted as the effect of the vacuum on the electron. 

In the preceeding sections we have shown the current status of quantum electrodynamical and related calculations in heavy hydrogenlike systems with its unique strong electric and magnetic fields. From our present experimental knowledge there is no contradiction to the theory of quantum electrodynamics as we use it nowadays. However, an increasing experimental precision may still point to deviations in the theory since in Lamb shift calculations the predictions are still at least one order of magnitude more precise than the best experimental values. On the other hand we... 

This second point of view can be illustrated by an example from the late 1940 s that will play an important role in this chapter. At that time the Schrodinger equation was well established, and its relativistic generalization, the Dirac equation, appeared to describe the spectrum of hydrogen perfectly, though the question of how to apply the Dirac equation to many-electron systems was still open. However, when more precise experiments were carried out, most notably by Lamb and Retherford [1], a small disagreement with theory was found. The attempt to understand this new physics stimulated theoretical efforts that led to the modern form of the first quantum field theory. Quantum Electrodynamics (QED). This small shift, which removes the Dirac degeneracy between the 2si/2 and states, known as the Lamb shift, is an example of a radiative correction. 

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