Local Equilibrium States in Quantum Field Theory in Curved Spacetime

Abstract

The present work concerns itself with the conceptual problem of assigning thermal parameters to states in quantum field theory in curved spacetime, and is based on the concept of local thermal equilibrium in the sense of Buchholz, Ojima and Roos. In this approach, point-like localized quantum fields, so called thermal observables, are used to attach thermal parameters to macroscopic systems, with the proviso that these systems do not deviate too far from thermal equilibrium. In contrast to many of the existing approaches, this allows for a conceptually clear description of non-equilibrium phenomena, for example in cosmology. The results are illustrated using the massless, conformally coupled, free scalar field. Initially, the structure of the set of thermal observables is discussed and it is found that in curved spacetime these objects do not form a vector space and must be chosen as linearly independent. However, there can be relations between the corresponding local thermal parameters which are induced by linear equations of state. It is shown that these relations lead to evolution equations for the local thermal parameters in curved spacetime. For thermal observables where no such linear relations hold, there exist states to which the corresponding local thermal parameters can be assigned in bounded regions in Minkowski spacetime. Using a natural assumption regarding the spectrum of the thermal observables, it is shown that states exist which are in equilibrium at any given point in a curved spacetime. Following on, it is argued that KMS states in stationary curved spacetimes may not be viewed in analogy to global thermal equilibrium states in Minkowski spacetime. The KMS parameter