By using a complex eld with a symmetric combination of electric and magnetic elds, a rstorder covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an in nite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserve...

The typical values of R = quantum energy/potential amplitude in electron energy of an incident radiation treated in quantum electrodynamics, an electric wiggler, and a magnetic wiggler are 108, 10–4 and 10–10, respectively. Therefore, the interaction of a free electron with these fields cannot be described with the same principle. The wave-function phase of the final state through a transition ...

Alexandre Blais, Jay Gambetta, A. Wallraff, D. I. Schuster, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA Département de Physique et Regroupement Québécois sur les Matériaux de Pointe, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1 Department of Physics, ETH Zurich, CH-8093 Zürich, S...