  The purpose of this paper is twofold. The first purpose is to find a fully
Poincare invariant solution of the Bethe-Salpeter equation for excited
quarkonia, however, the second, in fact, major focus is on the relevance of the
space-time metric choice and its imapact on the correct description of the
ground and all excited states. For the first time, we compare BSE solutions
defined independently with Euclidean and Minkowski metric. For this purpose,
the BSE is conventionally defined and solved in Euclidean space with two
versions of the propagator : the bare propagator and the confined form of the
quark propagator with complex conjugated poles. In both considered cases, there
is unexpected doubling of the spectrum, when comparing to the experiments as
well as to the solutions of the Schrodinger equation. The quark propagator with
complex conjugated singularities allows us to find the BSE solution directly in
Minkowski momentum space as well. We find the Minkowski space solution for
confining theories is not only numerically accessible, but provides a reliable,
albeit not yet completely satisfactory, description of the ground and excited
meson states.
