  The momentum space associated with "tachyonic particles" proves to be rather
intricate, departing very much from the ordinary dual to Minkowski space
directly parametrized by space-time translations of the Poincar\'e group. In
fact, although described by the constants of motion (Noether invariants)
associated with space-time translations, they depend non-trivially on the
parameters of the rotation subgroup. However, once the momentum space is
parametrized by the Noether invariants, it behaves exactly as that of ordinary
particles. On the other hand, the evolution parameter is no longer the one
associated with time translation, whose Noether invariant, $P_o$, is now a
basic one. Evolution takes place in a spatial direction. These facts not only
make difficult the computation of the corresponding representation, but also
force us to a sound revision of several traditional ingredients related to
Cauchy hypersurface, scalar product and, of course, causality. After that, the
theory becomes consistent and could shed new light on some special physical
situations like inflation or traveling inside a black hole.
