Quantum q-Field Theory: q-Schr\"{o}dinger and q-Klein-Gordon Fields

M.C. ROCCA; A. PLASTINO

EUROPHYSICS LETTERS

EPL ASSOCIATION

Lugar: Bologna; Año: 2017 vol. 118 p. 61004 - 61008

0295-5075

We show how to deal with the generalized q-Schr"{o}dinger and q-Klein-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 {f 948} (2016) 19; Nucl. Phys. A {f 955} (2016) 16].(See the Alice experiment of LHC).We develop here the quantum field theory (QFT) for the q-Schr"{o}dinger and q-Klein-Gordon fields, showing that both reduce to the customary Schr"{o}dinger and Klein-Gordon QFTs for q close to unity. Further, we analyze the q-Klein-Gordon field for $qgeq 1.15$ . In this case for$2q-1=n$ (n integer $geq 2$) and analytically compute the self-energy and the propagator up to second order.