  In this note we discuss the quantum mechanical three-body problem with
pairwise zero-range interactions in dimension three. We review the state of the
art concerning the construction of the corresponding Hamiltonian as a
self-adjoint operator in the bosonic and in the fermionic case. Exploiting a
quadratic form method, we also prove self-adjointness and boundedness from
below in the case of three identical bosons when the Hilbert space is suitably
restricted, i.e., excluding the "s-wave" subspace.
