2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/194863We derive the properties of hard thermal effective actions in gauge theories from the point of view of Schwinger's proper time formulation. This analysis is simplified by introducing a set of generalized energy and momenta which are conserved and are non-local in general. These constants of motion, which embody energy-momentum exchanges between the fields and the particles along their trajectories, can be related to a class of gauge invariant or covariant potentials in the hard thermal regime. We show that in this regime the generalized energy, which is non-local in general, generates the relevant non-local behavior of hard thermal effective actions which become local only in the static limit.6 pages, references added, version to appear in Physical Review DHigh Energy Physics - Theorytext