arXiv subjects
Publications and source records attributed to H. Thaler.
We study two possible prescriptions for AdS/CFT correspondence by means of functional integrals. The considerations are non-perturbative and reveal certain divergencies which turn out to be harmless, in the sense that reflection-positivity and conformal invariance are not destroyed.
We consider a relativistic Ansatz for the vacuum expectation values (VEVs) of a quantum field on a globally hyperbolic space-time which is motivated by certain Euclidean field theories. The Yang-Feldman asymptotic condition w.r.t. a "in"-field in a quasi-free representation of the canonic commutation relations (CCR) leads to a solution of this Ansatz for the VEVs. A GNS-like construction on a non-degenerate inner product space then gives local, covariant quantum fields with indefinite metric on a globally hyperbolic space-time. The non-trivial scattering behavior of quantum fields is analyzed by construction of the "out"-fields and calculation of the scattering matrix. A new combined effect of non-trivial quantum scattering and non-stationary gravitational forces is described for this model, as quasi-free "in"- fields are scattered to "out"-fields which form a non quasi-free representations of the CCR. The asymptotic condition, on which the construction is based, is verified for the concrete example of de Sitter space-time.