Two-potential approach to pair creation from the vacuum

Abstract

By applying a Foldy-Wouthuysen-like transformation and a low-momentum approximation to the usual quantum field theoretical Dirac Hamiltonian in one spatial dimension, we introduce a Hamiltonian for which the kinetic portion and the original potential are diagonal in the corresponding spinor space and a second potential occurs that is off diagonal. This two-potential Hamiltonian is applied to study the electron-positron pair creation process from the vacuum. Here the diagonal potential provides only the energy degeneracy of the lower and upper manifold of continuum states, which is one requirement for the permanent creation of particles. The off-diagonal potential actually triggers the creation process by providing the necessary coupling between the degenerate states. It also provides a concrete example of a model system for pair creation where the creation rate is perturbative in the coupling strength.