The gauged Thirring model in thermodynamic equilibrium

We study the gauged Thirring model (also known as Kondo model) in thermodynamic equilibrium using the Matsubara-Fradkin-Nakanishi formalism. In this formulation, both the temperature and the chemical potential are kept to be nonvanishing. Starting from the field equations, we write down the Dyson-Schwinger-Fradkin equations, the Ward-Fradkin-Takahashi identities, and expressions for the thermodynamical generating functional. We find the partition function of the theory and study some key features of its exact two-point Green functions, including the Landau-Khalatnikov/Fradkin transformations and some limiting cases of interest as well. In particular, we show that we can recover results from both the Schwinger and the Thirring models from the Kondo model in thermodynamic equilibrium.