Unified formalism for Thermal Quantum Field Theories: A geometric viewpoint

In this paper we study a unified formalism for Thermal Quantum Field Theories, i.e., for the Matsubara approach, Thermo Field Dynamics and the Path Ordered Method. To do so, we employ a mechanism akin to the Hawking effect which explores a relationship between the concept of temperature and spacetimes endowed with event-horizons. In particular, we consider an eight dimensional static spacetime, the so-called η-ξ spacetime, which we show to form an appropriate geometric background for generic Thermal Quantum Field Theories. Within this framework, the different formalisms of Thermal Field Theory are unified in a very natural way via various analytical continuations and the set of time-paths used in the Path Ordered Method is interpreted in geometric terms. We also explain reported inconsistencies inherent in the Thermo Field Dynamics through the appearance of horizons (and ensuing loss of information) in the η-ξ spacetime.