Factorization of self-adjoint operators by abstract Dirac operators and its application to second quantizations on Boson Fermion Fock spaces

We develop an abstract theory on factorization of nonnegative self-adjoint operators in terms of abstract Dirac operators. As an application, we obtain a necessary and sufficient condition for a second quantization on the abstract Boson-Fermion Fock space to be the square of a Dirac type operator and a result on uniqueness of such Dirac type operators