  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.
