We derive in a simple way the well-known hard thermal effective action for QCD through the application of the thermal operator to the zero temperature retarded Green’s functions. This derivation also clarifies the origin of important properties of the hard thermal effective action, such as the manifest Lorentz and gauge invariance of its integrand, by relating them directly to the properties of the corresponding zero temperature effective action in the hard regime.

• Received 8 March 2007

DOI:https://doi.org/10.1103/PhysRevD.76.025009