Eur. Phys. J. B 8, 439-443 (1999)
https://doi.org/10.1007/s100510050710

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

Received: 7 September 1998
Published online: 15 April 1999

Abstract

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.