Interacting quantum field theory on gravitational backgrounds

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Project objective

The unification of gravity and quantum physics is one of the main challenges of modern physics. A first step toward this aim would be the construction of interacting quantum field theories (QFT) on fixed classical gravitational backgrounds. Recently, in collaboration with Prof. K. Fredenhagen and Dr. M. Kohler, we stated what we call the 'microlocal spectrum condition' for selecting physical states. The condition is not empty since quasi-free Hadamard states satisfy it and with its use we proved, for the first time in this field, that the Wick polynomials of free fields are Wightman fields. In QFT on flat spaces several perturbative schemes have been developed and we follow now that of Epstein and Glaser. They construct and rigourously prove that each term of the perturbation series exists and fulfils locality, the main first principle of QFT. Our proposal is to generalize Epstein and Glaser scheme to curved space-times. Some preliminary attempts seem to indicate that our aim is reasonable since even for manifolds some of the steps in Epstein and Glaser work can be defined. In fact we are planning to use our previous work which ensures the existence of Wick polynomials and deals correctly with the spectrum condition on manifolds. However, several points are yet to be checked. Whence the existence of a renormalized perturbation theory is established, local renormalization conditions have to be found which fix the finite renormalization. Effects of curvature on observables quantities might be estimated and compared to esperiments.

Original text from CORDIS.

Participants

• Universität Hamburg · HamburgCoordinatorGermany
• Not availableCity levelItaly

Links

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