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MP: Theoretische und Mathematische Grundlagen der Physik

MP 9: Quantenfeldtheorie (axiomatisch)

MP 9.2: Vortrag

Dienstag, 21. März 2000, 15:15–15:30, W A317

Euclidean field theory on a sphere — •Dirk Schlingemann — The International Erwin Schrödinger Institute for Mathematical Physics (ESI), Boltzmanngasse 9, A-1090 Vienna

This talk is concerned with a structural analysis of euclidean field theories on the euclidean sphere. In the first part we give proposal for axioms for a euclidean field theory on a sphere in terms of C*-algebras.

Then, in the second part, we investigate the short-distance behavior of euclidean field theory models on the sphere by making use of the concept of scaling algebras, which has first been introduced by D. Buchholz, and R. Verch. We report on the expected statement that that scaling limit theories of euclidean field theories on a sphere are euclidean field theories on flat euclidean space.

Keeping in mind that the minkowskian analogue of the euclidean sphere is the de Sitter space, we discuss, in the third part, a Osterwalder-Schrader type construction scheme which assigns to a given euclidean field theory on the sphere a quantum field theory on de Sitter space. The reconstructed quantum field theoretical data fulfills the so called geodesic KMS condition in the sense of H. J. Borchers and D. Buchholz, i.e. for any geodesic observer the system looks like a system within a thermal equilibrium state.