Fermion Production in Classical Fields

Here, the formalism for the production of fermion-antifermion pairs by vacuum polarisation due to classical fields is investigated according to and extending Refs.^1,2. The issue of gauge invariance is discussed for the calculation of the expectation value for the number of produced pairs from the exact retarded and/or advanced propagator. These correlators are given as solutions of the equation of motion for the Dirac Green's functions in the classical field. The general characteristics of the two point functions in field configurations expected for ultrarelativistic heavy-ion collisions are lined out. Calculations for a model for the respective radiation field are presented in a covariant-derivative expansion scheme.