From noncommutative κ-Minkowski to Minkowski space-time

We show that free κ-Minkowski space field theory, discussed in the context of κ-Poincaré algebra and Doubly Special Relativity is equivalent to a relativistically invariant free field theory on Minkowski space-time. The field theory we obtain has in spectrum a relativistic mode of arbitrary mass m and a Planck mass tachyon. We show that while the energy-momentum for the relativistic mode is essentially the standard one, it diverges for the tachyon, so that there are no asymptotic tachyonic states in the theory. It also follows that the dispersion relation is not modified, so that, in particular, in this theory the speed of light is energy-independent.