# Thermal Field Theory of the Tsallis statistics

## TL;DR

This paper develops a quantum field theoretical framework for Tsallis statistics, deriving thermal two-point functions and applying them to compute the thermal mass of scalar bosons with phi^4 interaction.

## Contribution

It introduces the quantum field theory formulation of Tsallis distributions and demonstrates their role in thermal propagators, extending the conventional thermal field theory.

## Key findings

- Quantum Tsallis distributions appear in thermal propagators similarly to Boltzmann-Gibbs distributions.
- Derived the thermal two-point functions for Tsallis statistics.
- Calculated the thermal mass of scalar bosons in Tsallis statistics.

## Abstract

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.