Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-08-09
Annales Henri Poincare 3 (2002) 635-657
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
24 pages, Latex file, no figures
Scientific paper
The space of continuous states of perturbative interacting quantum field theories in globally hyperbolic curved spacetimes is determined. Following Brunetti and Fredenhagen, we first define an abstract algebra of observables which contains the Wick-polynomials of the free field as well as their time-ordered products, and hence, by the well-known rules of perturbative quantum field theory, also the observables (up to finite order) of interest for the interacting quantum field theory. We then determine the space of continuous states on this algebra. Our result is that this space consists precisely of those states whose truncated n-point functions of the free field are smooth for all n not equal to two, and whose two-point function has the singularity of a Hadamard fundamental form. A crucial role in our analysis is played by the positivity property of states. On the technical side, our proof involves functional analytic methods, in particular the methods of microlocal analysis.
Hollands Stefan
Ruan Weihua
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