Celestial Objects for Common Telescopes by T. Webb [orig. 1859]

By T. Webb [orig. 1859]

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Accelerator measurement of ge Consider an electron circulating in an accelerator ring of radius R. It is kept in → the ring by a constant external magnetic field B perpendicular to the plane of the Spin and Quantum Statistics 43 → ring. Its angular velocity ωC B is found by balancing the centrifugal with the Lorentz force. 8) γmc where γ = 1 − |v|2 c2 −1/2 , |v| = R |ωC |. 8). What does its spin S do? The → → precession of S around B is described by the so-called Bargmann–Michel–Telegdi (BMT) equation.

Experiment favours Schwinger’s result! This can be viewed – if one likes – as a high-precision confirmation of, among other things, the special theory of relativity. No matter whether electrons are treated non-relativistically or relativistically, we find that ge > 2! 2) of the quantum theory, and the effects of ‘supersymmetry breaking’ offer a handle on precision measurements of ge − 2; (see section 6). The fact that ge > 2 and the results in section 4 apparently imply that QED with non-relativistic matter ultimately only yields a mathematically meaningful description of physical systems if a (large, but finite) ultraviolet cutoff is imposed on the interactions between electrons and photons, no matter how small α is chosen.

7) 2mc and the total vector potential affecting orbital motion of the electrons is then given → → by ec A + m V = O(ge − 2) 0. The total Coulomb potential UCoulomb is invariant → under the transformation xj → yj , X j → Yj . 7) is approximately the same as the free energy in the laboratory frame → before the field B was turned on and ω = 0. This explains the Einstein–de Haas effect. → By measuring B and ω, one can determine ge ! 6)). Other effects based on the same ideas are encountered in cyclotron physics, two-dimensional electron gases exhibiting the quantum Hall effect, molecular and nuclear physics; see [27] and references given there.

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