**Abstract: **
A self-adjoint operator $A\not=A_0$ is said to be a singular
perturbation of the self-adjoint $A_0$ if the set
$\{\psi\in D(A)\cap D(A_0)\ :\ A\psi=A_0\psi\}$ is dense.
We show how to define all the singular perturbations
of a given $A_0$ and then we consider the particular case in
which $A_0$ is some free field Hamiltonian on Fock space.