Operator formalism of statistical mechanics of gauge theory in covariant gauges

An operator formalism of statistical mechanics of a gauge theory is presented in covariant gauges. We derive and propose a simple statistical operator e/sup -..beta..H-..pi..Q/sub c// instead of the usual form e/sup -betaH/ for the physical equilibrium system in a gauge theory, where Q/sub c/ is the Faddeev-Popov (FP) ghost charge. The diagrammatic expansion rule for the partition function is discussed in this formalism, and Bernard's suggestion of the strange rule that the FP ghost should be assigned a periodic temperature Green's function in spite of its Fermi statistics is confirmed rigorously. The gauge-fixing condition independence of the partition function and other physical quantities are also discussed.