State-Space Based Approach to Particle Creation in Spatially Uniform Electric Fields

Our formalism, described recently in (C. E. Dolby and S. F. Gull, Ann. Phys.293 (2001), 189-214.) is applied to the study of particle creation in spatially uniform electric fields, concentrating on the cases of a time-invariant electric field and a so-called adiabatic electric field. Several problems are resolved by incorporating the Bogoliubov coefficient approach and the tunnelling approach into a single consistent, gauge invariant formulation. The value of a time-dependent particle interpretation is demonstrated by presenting a coherent account of the time-development of the particle creation process, in which the particles are created with small momentum (in the frame of the electric field) and are then accelerated by the electric field to make up the bulge of created particles predicted by asymptotic calculations 2, 3]. An initial state comprising one particle is also considered, and its evolution is described as being the sum of two contributions: the sea of current produced by the evolved vacuum and the extra current arising from the initial particle state.