We show in this article that the Reeh-Schlieder property holds for states of quantum fields on real analytic curved spacetimes if they satisfy an analytic microlocal spectrum condition. This result holds in the setting of general quantum field theory, i.e. without assuming the quantum field to obey a specific equation of motion. Moreover, quasifree states… (More)
We show that as soon as a linear quantum field on a stationary spacetime satisfies a certain type of hyperbolic equation, the (quasifree) ground-and KMS-states with respect to the canonical time flow have the Reeh-Schlieder property. We also obtain an analog of Borchers' timelike tube theorem. The class of fields we consider contains the Dirac field, the… (More)
We give a noncommutative version of the complex projective space CP 2 and show that scalar QFT on this space is free of UV divergencies. The tools necessary to investigate Quantum fields on this fuzzy CP 2 are developed and several possibilities to introduce spinors and Dirac operators are discussed.
We introduce the notion of a semi-Riemannian spectral triple which generalizes the notion of spectral triple and allows for a treatment of semi-Riemannian manifolds within a noncommutative setting. It turns out that the relevant spaces in noncommutative semi-Riemannian geometry are not Hilbert spaces any more but Krein spaces, and Dirac operators are… (More)
Using the theory of quantized equivariant vector bundles over compact coadjoint orbits we determine the Chern characters of all non-commutative line bundles over the fuzzy sphere with regard to its derivation based differential calculus. The associated Chern numbers (topological charges) arise to be non-integer, in the commutative limit the well known… (More)
We relate high-energy limits of Laplace-type and Dirac-type operators to frame flows on the corresponding manifolds, and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators. Observables for the corresponding quantum systems are matrix-valued pseudodifferen-tial operators and therefore the system… (More)
We show that for compact orientable hyperbolic orbisurfaces, the Laplace spectrum determines the length spectrum as well as the number of singular points of a given order. Together with results of the first author in , this gives a full generalization of Huber's theorem to the setting of compact orientable hyperbolic orbisurfaces.
A well known result on pseudodifferential operators states that the noncommutative residue (Wodzicki residue) of a pseudodifferential projection vanishes. This statement is non-local and implies the regularity of the eta invariant at zero of Dirac type operators. We prove that in a filtered algebra the value of a projection under any residual trace depends… (More)
Let M be a connected Riemannian manifold and let D be a Dirac type operator acting on smooth compactly supported sections in a Hermitian vector bundle over M. Suppose D has a self-adjoint extension A in the Hilbert space of square-integrable sections. We show that any L 2-section ϕ contained in a closed A-invariant subspace onto which the restriction of A… (More)
We present a rigorous scheme that makes it possible to compute eigen-values of the Laplace operator on hyperbolic surfaces within a given precision. The method is based on an adaptation of the method of particular solutions to the case of locally symmetric spaces and on explicit estimates for the approximation of eigen-functions on hyperbolic surfaces by… (More)