Geometry and thermofields

Path integrals of matter fields on non-trivial euclidean background manifolds are investigated. Wave functions of fields on a surface which divides a manifold in two disjoint parts, are introduced. We derive two assumptions of thermofield dynamics: The insertion of the 'fictitious' system and the 'vacuum' vertical stroke0(β)>. Other manifolds, well known from quantum field theory in curved spacetime are studied; the euclidean sections of the Rindler wedge, Schwarzschild and de Sitter space. We show that the mixed state perceived by an observer in one of these backgrounds is of the same origin as the one in the finite temperature case. (orig.)