THE NEW QUANTUM ELECTRODYNAMICS

A recent discussion of its validity is given by Salpeter [118], who finds on the basis of the new quantum electrodynamics, the need for a very small extra term for levels in hydrogen, — (4Ra3ra/37msAf). 

The confirmation by Lamb and Retherford of the inadequacy of the Dirac theory stimulated a re-examination of a theoretical problem to which only a very incomplete solution had so far been found the problem of the interaction between charged particles and the electromagnetic field. We shall briefly refer to the problem as it presented itself in classical physics, and then (following Weisskopf [135]) notice the further difficulties which the quantum theory introduces. Finally we shall see how these difficulties have been circumvented by the new quantum electrodynamics, and how a small correction is thereby introduced to the energy levels predicted by Dirac s theory. The new theory, however, is not a complete and logically satisfactory solution to the problems we shall state a difficulty of principle remains now, as formerly. 

The suggestion of Breit [22] that the magnetic moment of the electron differs from one Bohr magneton substantially resolved the major hyperfine structure discrepancy. In section 9.7 we mentioned that the new quantum electrodynamics, through the relativistic treatment of renormalization of mass, predicts a correction to the Dirac value of the electron magnetic moment. To second order in the perturbation approach, the correction factor is (l-foc/27r). A higher order... 

Corrections to the above formulae are introduced by the new quantum electrodynamics. There is no spectacular splitting of levels since there is no degeneracy, but in so far as AW depends on it is clear that the anomalous magnetic moment of the electron will influence the result. Calculations to order a3, relative to the gross structure, have been made by Karpins and Klein [68]. These authors obtain the result... 

At the end of Section 8.16 we mentioned that the Fock representation avoids the use of multiple integrations of coordinate space when dealing with the many-body problem. We can see here, however, that the new method runs into complications of its own To handle the immense bookkeeping problems involved in the multiple -integrals and the ordered products of creation and annihilation operators, special diagram techniques have been developed. These are discussed in Chapter 11, Quantum Electrodynamics. The reader who wishes to study further the many applications of these techniques to problems of quantum statistics will find an ample list of references in a review article by D. ter Haar, Reports on Progress in Physics, 24,1961, Inst, of Phys. and Phys. Soc. (London). 

The statement that quantum electrodynamics is invariant under such a spatial inversion (parity operation) can be taken as the statement that there exist new field operators >p (x ) and A x ) expressible in terms of tji(x) and Au(x) which satisfy the same commutation rules and equations of motion in terms of s as do ift(x) and A x) written in terms of x. In fact one readily verifies that the operators... 

As indicated at the beginning of the last section, to say that quantum electrodynamics is invariant under space inversion (x = ijX) means that we can find new field operators tfi (x ),A v x ) expressible in terms of fj(x) and A nix) which satisfy the same equations of motion and commutation rules with respect to the primed coordinate system (a = igx) as did tf/(x) and Av(x) in terms of x. Since the commutation rules are to be the same for both sets of operators and the set of realizable states must be invariant, there must exist a unitary (or anti-unitary) transformation connecting these two sets of operators if the theory is invariant. For the case of space inversions, such a unitary operator is... 

Why this emphasis Schweber has portrayed Slater as a man who developed a deep feeling of both inferiority and competitiveness toward his European mentors and peers in the fields of atomic physics and quantum electrodynamics. Slater was not alone in this reaction, as Henry James made clear. Slater, like other American physicists and chemists, used his influence in Boston, New York, and Washington circles, as well as his position within his own institution, to build up American science in an area where Americans could take a competitive lead. 107 Donnan had written Lewis in 1921 that "you are making old Europe sit up some. If it wasn t for Planck, Einstein, Rutherford, and Bragg, we should be in a bad way." 108 But it was not enough for Europeans to sit up "some" they must be made to gawk. 

We derived (3.54) earlier from our semiclassical treatment, but (3.55) is new information. Quantum electrodynamics (Merzbacher, Chapter 22) confirms the correctness of (3.55). 

The degree of precision of the quantized Hall effect has amaz-cd even the experts. Measured values of the Hall resistance at various integer plateaus are accurate to about one part in six million. The effect can be used to construct a laboratory standard of electrical resistance that is much more accurate than Ihe standard resistors currently in use. Authorities also observe that, if the quantized Hall effect is combined with a new calibration ol an absolute resistance standard, it should he able lo yield an improved measurement of the fundamental dimensionless constant of quantum electrodynamics. Ihe fine-structure constant or. 

Clarke, J. et al. Quantum Mechanics of a Macroscopic Variable The Phase Difference of a Josephson Inaction, Science, 992 (February 26, 1988). Colieii-Tauuuudii, C., Dupont-Roc, J, and G. Grynberg Photons and Atoms Quantum Electrodynamics. Wiley, New York. NY, 1989. 

The electromagnetic helicity has also been studied by Evans [54—57], especially its consequences for his new non-Abelian SO(3) gauge version of QED (quantum electrodynamics). 

The principal purpose here has been to demonstrate what sort of electroweak interaction physics may be required for the existence of an 0(3)b theory of quantum electrodynamics on the low-energy physical vacuum. This demonstrates that an extended standard model of electroweak interactions can support such a theory with the addition of new physics at high energy. 

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. 

Abstract. A review is given of the latest adjustment of the values of the fundamental constants. The new values are recommended by the Committee on Data for Science and Technology (CODATA) for international use. Most of the fundamental constants are obtained by the comparison of the results of critical experiments and the corresponding theoretical expressions based on quantum electrodynamics (QED). An important case is the Rydberg constant which is determined primarily by precise frequency measurements in hydrogen and deuterium. 

Abstract. Using Doppler-tuned fast-beam laser spectroscopy the ls2p 3Po - 3Pi fine structure interval in 24Mg10+ has been measured to be 833.133(15) cm-1. The calibration procedure used the intercombination ls2s 1So - ls2p 3Pi transition in 14N5+. The result tests quantum-electrodynamic and relativistic corrections to high precision calculations, which will be used to obtain a new value for the fine structure constant from the fine structure of helium. 

Abstract. Absolute measurements of the energies of helium-like vanadium resonances on an electron beam ion trap (EBIT) axe reported. The results agree with recent theoretical calculations and the experimental precision (27-MO ppm) lies at the same level as the current uncertainty in theory (0.1 eV). The measurements represent a 5.7%-8% determination of the quantum electrodynamics (QED) contribution to the transition energies and are the most precise measurements of the helium-hke resonances in the Z = 19—31 range. These are the first precision X-ray measurements on the National Institute of Standards and Technology EBIT and strongly commend the EBIT as a new spectroscopic source for QED investigations. 

The theorists, who never lack for ingenuity and inventiveness, no longer seem to be writing about the X0 particle. However, there have been several discussions about a new phase of quantum electrodynamics, an even more radical interpretation of the G. S. I. results. [21]... 

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