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

Abstract

We show how to deal with the generalized q-Schrödinger and q-Klein-Gordon fields in a variety of scenarios. These q-fields are meaningful at very high energies (TeVs) for high ones (GeVs) for and at low energies (MeVs) for (Plastino A. and Rocca M., Nucl. Phys. A, 948 (2016) 19; Plastino A. et al., 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 (n integer ≥ 2) and analytically compute the self-energy and the propagator up to second order.