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Hadamard states, adiabatic vacua and the construction of physical states for scalar quantum fields on curved spacetime. (English) Zbl 0869.53053
Once for a quantum field on a curved spacetime, the algebra $$A$$ of observables has been constructed, the states can be defined as the normalized positive linear functionals on $$A$$. However, not every mathematical state is physically realizable. On Minkowski space it is understood that the physical states are exactly the elements of the “folium” (=quasiequivalence class) of the vacuum state. On a curved background, however, there is no vacuum state and a generally accepted method of how to determine the physical state does not exist. In the article under review, the author gives a detailed and comprehensive report on the partial results that have been achieved to overcome this problem. Throughout the Klein-Gordon equation is considered on a globally hyperbolic spacetime.