Tachyons in “momentum-space” representation

Abstract

Obtaining the momentum space associated with tachyonic “particles” from the Poincaré group manifold proves to be rather intricate, departing very much from the ordinary dual to Minkowski space directly parametrized by space-time translations of the Poincaré 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 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.