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Transformation laws of the Newman-Penrose field variables
ANNALS OF PHYSICS97, 578-580 (1976)
Abstracts
of Papers
to
Appear
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Quantum Electrodynamic Corrections to the 23Sl + I’S, + One Photon Transition Rate in Helium and Helium-like Ions. EDWARD J. KELSEY. Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742, and Behlen Laboratory of Physics, Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588. The order (Zc@, ~(ZOI)*, and a(Z4)4 log(Zor) energy denominator and recoil corrections to the leading order (201)~ decay amplitude for the 23S, + lY& + one photon transition are considered. It is found that order o1(Z@ terms arise in the individual diagrams but exactly cancel upon summation. In view of the results of this and other recent theoretical work it is concluded that the rates predicted by pure quantum electrodynamics are known to considerable precision. The recent discrepancy between theory and experiment in the decay rate for several helium-like ions appears to have been resolved by placing the detector farther downstream from the foil where the metastable states are produced. At present, all the experimental values are in good agreement with the theory. Transformation Laws of the Newman-Penrose Field Variables. M. CARMELI AND M. KAYE. Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84120, Israel. The transformation laws of all the Newman-Penrose gravitational field variables under the six parameter proper, orthochronous, Lorentz group are given. The method used here utilizes results obtained by Carmeli in his gauge theoretic formulation of the gravitational field equations. Scale Transformations for Renormalized Field Operators: Discussion of the Soluble Model. J. LUKIERSKI, International Centre for Theoretical Physics, Trieste, Italy, and A. OGIELSKL Institute of Theoretical Physics, University of Wroclaw, Poland. We discuss the operator formulation of the Zachariasen-Thirring model, describing the chain approximation to the propagator (the sum of three-particle massless bubbles) in massless hv4 theory. Such a model is formally scale-invariant and explicitly soluble. All intermediate steps of conventional renormalization procedure: regularization, introduction of appropriate counterterms and cut-off free limit, are explicitly performed. In every step the scaling properties are discussed and respective dilatation currents are written down. After the proper choice of scale transformations for the renormalized field operator, we obtain the nonlocal dilatation current, defining the renormalized dilatation generator D&t). In the cut-off free limit rl+ GO the ET commutator of DnR(t) with renormalized field operators reproduces the Callan-Symanzik modification of “naive” canonical scale transformations. The renormalized scale transformations coincide in the cut-off free limit with renormalized dimensional transformations and define the exact symmetry of the renormalized theory. Recoil Corrections to Elastic Electron Scattering in the Breit Approximation. ment of Physics, Brown University, Providence, Rhode Island 02912.
J. L. FRIAR. Depart-
Recoil corrections to the cross-sections for elastic electron scattering from spin-0 nuclei are investigated in the Breit approximation. The form of the scattering amplitude in first- and secondCopyright All rights
0 1976 by Academic Press, Inc. of reproduction in any form reserved.
578
Abstracts
of Papers
to
Appear
in Future
Issues
Quantum Electrodynamic Corrections to the 23Sl + I’S, + One Photon Transition Rate in Helium and Helium-like Ions. EDWARD J. KELSEY. Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742, and Behlen Laboratory of Physics, Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588. The order (Zc@, ~(ZOI)*, and a(Z4)4 log(Zor) energy denominator and recoil corrections to the leading order (201)~ decay amplitude for the 23S, + lY& + one photon transition are considered. It is found that order o1(Z@ terms arise in the individual diagrams but exactly cancel upon summation. In view of the results of this and other recent theoretical work it is concluded that the rates predicted by pure quantum electrodynamics are known to considerable precision. The recent discrepancy between theory and experiment in the decay rate for several helium-like ions appears to have been resolved by placing the detector farther downstream from the foil where the metastable states are produced. At present, all the experimental values are in good agreement with the theory. Transformation Laws of the Newman-Penrose Field Variables. M. CARMELI AND M. KAYE. Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84120, Israel. The transformation laws of all the Newman-Penrose gravitational field variables under the six parameter proper, orthochronous, Lorentz group are given. The method used here utilizes results obtained by Carmeli in his gauge theoretic formulation of the gravitational field equations. Scale Transformations for Renormalized Field Operators: Discussion of the Soluble Model. J. LUKIERSKI, International Centre for Theoretical Physics, Trieste, Italy, and A. OGIELSKL Institute of Theoretical Physics, University of Wroclaw, Poland. We discuss the operator formulation of the Zachariasen-Thirring model, describing the chain approximation to the propagator (the sum of three-particle massless bubbles) in massless hv4 theory. Such a model is formally scale-invariant and explicitly soluble. All intermediate steps of conventional renormalization procedure: regularization, introduction of appropriate counterterms and cut-off free limit, are explicitly performed. In every step the scaling properties are discussed and respective dilatation currents are written down. After the proper choice of scale transformations for the renormalized field operator, we obtain the nonlocal dilatation current, defining the renormalized dilatation generator D&t). In the cut-off free limit rl+ GO the ET commutator of DnR(t) with renormalized field operators reproduces the Callan-Symanzik modification of “naive” canonical scale transformations. The renormalized scale transformations coincide in the cut-off free limit with renormalized dimensional transformations and define the exact symmetry of the renormalized theory. Recoil Corrections to Elastic Electron Scattering in the Breit Approximation. ment of Physics, Brown University, Providence, Rhode Island 02912.
J. L. FRIAR. Depart-
Recoil corrections to the cross-sections for elastic electron scattering from spin-0 nuclei are investigated in the Breit approximation. The form of the scattering amplitude in first- and secondCopyright All rights
0 1976 by Academic Press, Inc. of reproduction in any form reserved.
578