2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201471Through the application of the thermal operator to the zero temperature retarded Green's functions, we derive in a simple way the well known hard thermal effective action in QCD. By relating these functions to forward scattering amplitudes for on-shell particles, 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.6 pages, contribution of the quarks to the effective action included and one reference added, version to be published in Phys. Rev. DHigh Energy Physics - Theorytext