  Classical and quantum Tsallis distributions have been widely used in many
branches of natural and social sciences. But, the quantum field theory of the
Tsallis distributions is relatively a less explored arena. In this article we
derive the expression for the thermal two-point functions for the Tsallis
statistics with the help of the corresponding statistical mechanical
formulations. We show that the quantum Tsallis distributions used in the
literature appear in the thermal part of the propagator much in the same way
the Boltzmann-Gibbs distributions appear in the conventional thermal field
theory. As an application of our findings, thermal mass of the real scalar
bosons subjected to phi^4 interaction has been calculated in the Tsallis
statistics.
