More transition amplitudes on the Riemann sphere

We consider a conformal field theory for bosons on the Riemann sphere. Correlation functions are defined as singular limits of functional integrals. The main result is that these amplitudes define transition amplitudes, that is multilinear Hilbert-Schmidt functionals on a fixed Hilbert space.Comment: 20 page

Representation theory of the stabilizer subgroup of the point at infinity in Diff(S^1)

The group Diff(S^1) of the orientation preserving diffeomorphisms of the circle S^1 plays an important role in conformal field theory. We consider a subgroup B_0 of Diff(S^1) whose elements stabilize "the point of infinity". This subgroup is of interest for the actual physical theory living on the punctured circle, or the real line. We investigate the unique central extension K of the Lie algebra of that group. We determine the first and second cohomologies, its ideal structure and the automorphism group. We define a generalization of Verma modules and determine when these representations are irreducible. Its endomorphism semigroup is investigated and some unitary representations of the group which do not extend to Diff(S^1) are constructed.Comment: 34 pages, no figur

Von der preussischen Kommission zur Erforschung der Reformation und Gegenreformation. II. Instruktion für die Arbeiten der bibliographischen Abteilung

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