  We study the Hamiltonian for a Bose gas in three dimensions of $N \geq 3$
spinless particles interacting via zero-range or contact interactions. Such
interactions are described by (singular) boundary conditions satisfied at the
coincidence hyperplanes, i.e., when the coordinates of two particles coincide.
It is known that if one imposes the same kind of boundary condition of the
one-body problem with a point interaction then one is inevitably led to a
Hamiltonian unbounded from below and therefore unstable. This is due to the
fact that the interaction becomes too strong and attractive when the
coordinates of three or more particles coincide. In order to avoid such
instability property, we develop a suggestion formulated by Minlos and Faddeev
in 1962 and introduce a slightly modified boundary condition which reduces the
strength of the interaction when the positions of the particles $i, j$ coincide
in the following cases: a) a third particle approaches the common position of
$i$ and $j$; b) two other particles approach to each other. In all the other
cases the usual boundary condition is restored. Following a quadratic form
approach, we prove that the Hamiltonian characterized by such modified boundary
condition is self-adjoint and bounded from below. We also show that the N-body
Hamiltonian with contact interactions obtained years ago by Albeverio,
H{\o}egh-Krohn and Streit using the theory of Dirichlet forms (J. Math. Phys.,
18, 907--917, 1977) is a special case of our Hamiltonian.
