2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196103Using the mixed space representation (t,p) in the context of scalar field theories, we prove in a simple manner that the Feynman graphs at finite temperature are related to the corresponding zero temperature diagrams through a simple thermal operator, both in the imaginary time as well as in the real time formalisms. This result is generalized to the case when there is a nontrivial chemical potential present. Several interesting properties of the thermal operator are also discussed.20 pages, seven figuresHigh Energy Physics - TheoryHigh Energy Physics - Phenomenologytext