FERMIONIC AND BOSONIC PAIR CREATION IN AN EXTERNAL ELECTRIC-FIELD AT FINITE-TEMPERATURE USING THE FUNCTIONAL SCHRODINGER REPRESENTATION

We solve the time evolution of the density matrix both for fermions an d bosons in the presence of a homogeneous but time-dependent external electric field. The number of particles produced by the external field , as well as their distribution in momentum space, is found for finite times. Furthermore, we calculate the probability of finding a given n umber of particles in the ensemble. In all cases, there is a nonvanish ing thermal contribution. The bosonic and the fermionic density matric es are expressed in a ''functional field basis.'' This constitutes an extension of the ''field basis'' concept to fermions.