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We solve the time evolution of the density matrix both for fermions andbosons in the presence of a homogeneous but time dependent external electricfield. The number of particles produced by the external field, as well as theirdistribution in momentum space is found for finite times. Furthermore, wecalculate the probability of finding a given number of particles in theensemble. In all cases, there is a nonvanishing thermal contribution. Thebosonic and the fermionic density matrices are expressed in a "functional fieldbasis". This constitutes an extension of the "field basis" concept to fermions.Comment: 28 pages, latex, uses psfig and epsf, 4 figures included, minor  change

Fermionic and bosonic pair creation in an external electric field at finite temperature using the functional Schrödinger representation