Tsallis' Quantum q-Fields

TL;DR

This paper extends classical quantum field equations to a Tsallis' q-framework, introducing q-generalizations of key equations and fields, and establishing corresponding quantum field theories applicable across various energy scales.

Contribution

It provides a systematic formulation of q-quantum field theories for multiple fundamental fields, including new q-Yang-Mills equations, and explores their high-energy relevance.

Findings

q-fields are q-exponential functions of linear fields' logarithms.

Quantum equations are generalized to include q-parameters, linking to high-energy physics.

The framework applies to different energy scales, from MeV to TeV.

Abstract

We generalize several well known quantum equations to a Tsallis' q-scenario, and provide a quantum version of some classical fields associated to them in recent literature. We refer to the q-Schr\"odinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, [Phys. Rev. Lett. {\bf 106}, 140601 (2011), EPL {\bf 118}, 61004 (2017) and references therein]. Also, we introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and not-Abelian instances. We show how to define the q-Quantum Field Theories corresponding to the above equations, introduce the pertinent actions, and obtain motion equations via the minimum action principle. These q-fields are meaningful at very high energies (TeVs) for $q=1.15$, high ones (GeVs) for $q=1.001$, and low energies (MeVs)for $q=1.000001$ [Nucl. Phys. A {\bf 955} (2016) 16 and references therein]. (See the Alice experiment of LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields' logarithms.