Quantum q-field theory: Q-Schrödinger and q-Klein-Gordon fields

Abstract

We show how to deal with the generalized q-Schrödinger and qKlein-Gordon fields in a variety of scenarios. These q-fields are meaningful at very high energies (TeVs) for for q = 1.15, high ones (GeVs) for q = 1.001, and low energies (MeVs)for q = 1.000001 [Nucl. Phys. A 948 (2016) 19; Nucl. Phys. A 955 (2016) 16]. (See the Alice experiment of LHC). We develop here the quantum field theory (QFT) for the q-Schrödinger and q-Klein-Gordon fields, showing that both reduce to the customary Schrödinger and Klein-Gordon QFTs for q close to unity. Further, we analyze the q-Klein-Gordon field for q ≥ 1.15 . In this case for 2q − 1 = n (n integer ≥ 2) and analytically compute the self-energy and the propagator up to second order.