  Within the framework of Tsallis statistics with q ~ 1, we construct a
perturbation theory for treating relativistic quantum field systems. We find
that there appear initial correlations, which do not exist in the
Boltzmann-Gibbs statistics. Applying this framework to a quark-gluon plasma, we
find that the so-called thermal masses of quarks and gluons are smaller than in
the case of Boltzmann-Gibbs statistics.
