Quantum relativistic theory of an electron in terms of local observables
Laboratoire de Physico-Chimie Théorique, ESPCI, 10 rue Vauquelin, 75231
Paris Cedex 05, France et La Cointrie,
61340 Saint Aubin des Grois, France
Published online: 15 April 1999
Dirac equation is reformulated in terms of real local observables, which are mean values of the wave function . The quadrivector current is shown to be a function of the potential vector and of other local observables. The equations describe the evolution of a four dimensional system T, X, Y, Z, and of two scalars, in the coordinate system ct, x, y, z. The current is proportional to the T vector. The Z vector is associated with the spin of the electron. Energy and gauge transformations correspond to rotations in the plane (X, Y). In the presence of a static field, the (real) solutions of the equations appear as eigenfunctions associated with energy eigenvalues.
PACS: 03.65.Bz – Foundations, theory of measurement, miscellaneous theories (including Aharonov Bohm effect, Bell inequalities, Berry's phase) / 03.65.Pm – Relativistic wave equations / 05.30.-d – Quantum statistical mechanics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999