  The problem of a relativistic bound-state system consisting of two scalar
bosons interacting through the exchange of another scalar boson, in 2+1
space-time dimensions, has been studied. The Bethe-Salpeter equation (BSE) was
solved by adopting the Nakanishi integral representation (NIR) and the
Light-Front projection. The NIR allows us to solve the BSE in Minkowski space,
which is a big and important challenge, since most of non-perturbative
calculations are done in Euclidean space, e.g. Lattice and Schwinger-Dyson
calculations. We have in this work adopted an interaction kernel containing the
ladder and cross-ladder exchanges. In order to check that the NIR is also a
good representation in 2+1, the coupling constants and Wick-rotated amplitudes
have been computed and compared with calculations performed in Euclidean space.
Very good agreement between the calculations performed in the Minkowski and
Euclidean spaces has been found. This is an important consistence test that
allows Minkowski calculations with the Nakanishi representation in 2+1
dimensions. This relativistic approach will allow us to perform applications in
condensed matter problems in a near future.
