Photon mass 0 electrodynamics

Photon mass is shown to be self-consistent with 0(3) electrodynamics by considering the 0(3) Lagrangian [6] in reduced units ... 

The Lagrangian (850) shows that 0(3) electrodynamics is consistent with the Proca equation. The inhomogeneous field equation (32) of 0(3) electrodynamics is a form of the Proca equation where the photon mass is identified with a vacuum charge-current density. To see this, rewrite the Lagrangian (850) in vector form as follows ... 

Concluding Remarks.—We have come to the end of our exposition of some aspects of quantum electrodynamics. We have not delved in some of the more technical and difficult facets of the subject matter. Mention should, however, be made of what some of the difficulties are. Foremost at the technical level is perhaps the role played by the infrared divergences. The fact that the photon has zero mass not only gives rise to divergences in various matrix elements,20 but also implies... 

It is seen that the acquisition of mass by the photon is the result of an equation of superconductivity, and this is, of course, the basis of spontaneous symmetry breaking and the Higgs mechanism (Section XIV). Beltrami equations account for all these phenomena, and are foundational in nature. Note that the London equation (919) is not gauge-invariant on the U(l) level because aphysical gauge-invariant current is proportional to the vector potential, which, in the received view, is gauge-noninvariant. This is another flaw of U(l) electrodynamics in the... 

We will review here experimental tests of quantum electrodynamics (QED) and relativistic bound-state formalism in the positron-electron (e+,e ) system, positronium (Ps). Ps is an attractive atom for such tests because it is purely leptonic (i.e. without the complicating effects of nuclear structure as in normal atoms), and because the e and e+ are antiparticles, and thus the unique effects of annihilation (decay into photons) on the real and imaginary (related to decay) energy levels of Ps can be tested to high precision. In addition, positronium constitutes an equal-mass, two-body system in which recoil effects are very important. 

See J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962) J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons (Addison-Wesley, Cambridge, Mass., 1955). 

Cold, trapped HD+-ions are ideal objects for direct spectroscopic tests of quantum-electrodynamics, relativistic corrections in molecules, or for determining fundamental constants such as the electron-proton mass ratio. It is also of interest for many applications since it has a dipole moment. The potential of localizing trapped ions in Coulomb crystals has been demonstrated recently with spectroscopic studies on HD+ ions with sub-MHz accuracy. The experiment has been performed with 150 HD+ ions which have been stored in a linear rf quadrupole trap and sympathetically cooled by 2000 laser-cooled Be+ ions. IR excitation of several rovibrational infrared transitions has been detected via selective photodissociation of the vibra-tionally excited ions. The resonant absorption of a 1.4/itm photon induces an overtone transition into the vibrational state v = A. The population of the V = A state so formed is probed via dissociation of the ion with a 266 nm photon leading to a loss of the ions from the trap. Due to different Franck-Condon factors, the absorption of the UV photon from the v = A level is orders of magnitude larger than that from v = 0. 

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