The Bethe-Peierls asymptotic approach which models pairwise short-range
forces by contact conditions is introduced in arbitrary representation for
spatial dimensions less than or equal to 3. The formalism is applied in various
situations and emphasis is put on the momentum representation. In the presence
of a transverse harmonic confinement, dimensional reduction toward
two-dimensional (2D) or one-dimensional (1D) physics is derived within this
formalism. The energy theorem relating the mean energy of an interacting system
to the asymptotic behavior of the one-particle density matrix illustrates the
method in its second quantized form. Integral equations that encapsulate the
Bethe-Peierls contact condition for few-body systems are derived. In three
dimensions, for three-body systems supporting Efimov states, a nodal condition
is introduced in order to obtain universal results from the Skorniakov
Ter-Martirosian equation and the Thomas collapse is avoided. Four-body bound
state eigenequations are derived and the 2D '3+1' bosonic ground state is
computed as a function of the mass ratio
