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 to them in recent literature. We refer to the q-Schrödinger, 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.

References in corpus (6)

• K*(892)${}^0$ and $\Phi$(1020) production in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
• Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems?
• From the hypergeometric differential equation to a non linear Schrödinger one
• q-Gamow States as continuous linear functionals on analytical test functions
• q-Gamow States for intermediate energies
• Classical and \textcolor{blue}{Quantum} Field-Theoretical approach to the non-linear q-Klein-Gordon Equation

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