  Here, I focus on the use of microscopic, few-body techniques that are
relevant in the many-body problem. These methods can be divided into indirect
and direct. In particular, indirect methods are concerned with the
simplification of the many-body problem by substituting the full, microscopic
interactions by pseudopotentials which are designed to reproduce collisional
information at specified energies, or binding energies in the few-body sector.
These simplified interactions yield more tractable theories of the many-body
problem, and are equivalent to effective field theory of interactions. Direct
methods, which so far are most useful in one spatial dimension, have the goal
of attacking the many-body problem at once by using few-body information only.
Here, I will present non-perturbative direct methods to study one-dimensional
fermionic and bosonic gases in one dimension.
