2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/47712This paper discusses the analytic continuation in the thermal field theory by using the theory of $η-ξ$ spacetime. Taking a simple model as example, the $2\times 2$ matrix real-time propagator is solved from the equation obtained through continuation of the equation for the imaginary-time propagator. The geometry of the $η-ξ$ spacetime plays important role in the discussion.9 pages Reoort-no: HZPP-9803High Energy Physics - Phenomenologytext