A modern guide to 𝜃-Poincaré

Abstract

Motivated by the recent interest in underground experiments phenomenology (see Refs. 1–3), we review the main aspects of one specific noncommutative space–time model, based on the Groenewold–Moyal plane algebra, the [Formula: see text]-Poincaré space–time. In the [Formula: see text]-Poincaré scenario, the Lorentz co-algebra is deformed introducing a noncommutativity of space–time coordinates. In such a theory, a new quantum field theory in noncommutative space–time can be reformulated. Tackling on several conceptual misunderstanding and technical mistakes in the literature, we will focus on several issues such: (i) the construction of fields theories in [Formula: see text]-Poincaré; (ii) the unitarity of the S-matrix; (iii) the violation of locality, (iv) the violation of the spin-statistic theorem and the Pauli principle; (v) the observables for underground experiments.