Tsallis' quantum q-fields

Abstract

We generalize several well known quantum equations to a Tsallis' q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schródinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601 (2011), EPL 118, 61004 (2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle. These q-fields are meaningful at very high energies (TeV scale) for q = 1.15, high energies (GeV scale) for q = 1.001, and low energies (MeV scale) for q = 1.000001 [Nucl. Phys. A 955 (2016) 16 and references therein]. (See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields' logarithms.