From noncommutative kappa-Minkowski to Minkowski space-time

TL;DR

This paper demonstrates that free $appa$-Minkowski space field theory can be reformulated as a relativistically invariant, non-local field theory on Minkowski space, with specific spectral properties and no energy-dependent speed of light.

Contribution

It establishes an equivalence between $appa$-Minkowski space field theory and a relativistic non-local Minkowski space theory, clarifying its spectral and dynamical features.

Findings

Spectrum includes a relativistic mode and a Planck mass tachyon.

Energy-momentum for the relativistic mode matches standard form.

No asymptotic tachyonic states due to divergent energy-momentum.

Abstract

We show that free $\kappa$-Minkowski space field theory is equivalent to a relativistically invariant, non local, 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.