Non-extensive ThermoField Dynamics: applications to boson and fermion fields

Abstract It is noted that Tsallis statistics (TS) in quantum field theory remains insufficiently unexplored. TS are particularly suited for systems characterized by long-range correlations, intrinsic fluctuations, non-Markovian behavior, and non-equilibrium features. In low-energy quantum electrodynamics (QED), the Tsallis parameter ( q -parameter) accounts for non-equilibrium effects in the photon medium, while in high-energy quantum chromodynamics (QCD), it reflects the power-law behavior observed in particle spectra. In this work, we introduce a non-extensive structure via the Bogoliubov transformation in ThermoField Dynamics (TFD), where q -dependent elements define the q -thermal vacuum and generate all components of the Tsallis-TFD propagator. We construct this propagator and consider two applications: thermal photon–photon interactions in low-energy QED using a scalar Tsallis propagator, and the phase of electron–positron pair annihilation into hadrons via single photon exchange in high-energy QCD using a fermion Tsallis propagator. Our analysis illustrates that the thermal part of the Tsallis-TFD propagator remains structurally similar to the conventional TFD result based on Boltzmann–Gibbs statistics. Moreover, the photon–photon interaction and the phase of electron–positron pair annihilation into hadrons exhibit a shift in their curves as the q -parameter increases at finite temperature. These results indicate that thermal effects depend on both the temperature and the q -parameter.