Production of fermion pairs associated with decay of a metastable vacuum

A study is made of the production of fermion pairs associated with the tunneling process that leads to decay of a metastable vacuum in field theory. The technique of nonunitary Bogolyubov transformations is developed. Expressions are obtained for the spectrum of the produced fermions. The spectrum of fermion pairs produced when there is homogeneous decay of a metastable vacuum is found as an example.