Zero energy and thermodynamic equilibrium

Using path integral techniques, it is shown that the real time formalism for finite temperature field theory requires an extra Feynman rule for Feynman diagrams carrying zero-external energies. This is related to a general principle governing the use of equilibrium finite temperature field theory. It is shown that only with this extra Feynman rule does the real time formalism become consistent for zero energy calculations. It is also used to understand the problem of the lack of analyticity at zero external four-momenta encountered in finite temperature field theory diagrams.