Feynman rules for gauge theories at finite temperature

Feynman's functional formulation of statistical mechanics is used to study general-relativistic quantum field theories at finite temperature. The techniques are then applied to gauge theories. The partition function $\mathrm{Tr}{e}^{-\beta H}$ is discovered to be a gauge-dependent quantity which is meaningless in most gauges. Instead, we define a physically meaningful partition function which is gauge-invariant and only equal to $\mathrm{Tr}{e}^{-\beta H}$ in certain "physical" gauges. Feynman rules for this partition function and for finite-temperature Green's functions are derived for a general gauge.