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The Einstein – Hilbert action of General Relativity is not fit to describe quantum fluctuations of the metrics as it does not restrict either large fluctuations or fast varying ones. Therefore, it defines at best an effective theory which, of course, is tremendously successful. A hint how to construct a true and well defined `microscopic’ gravitation theory is provided by the fact that there are fermions in Nature. Fermions require that the field variables to be used are the vierbein and the Lorentz spin connection. This leads to Cartan’s formulation of General Relativity, but field fluctuations are not restricted there either because none of the possible general covariant action terms is sign-definite. A way out is to present the vierbein as a bilinear "current" of more fundamental fermion (spinor) fields. Path integrals over Grassmann variables are well defined for whatever sign of the fermion action. We suggest that in the ultraviolet limit quantum gravity possesses only spinor and gauge field degrees of freedom, like in the Standard Model. The theory can be easily regularized by putting it on a space lattice. It is explicitly invariant under local Lorentz transformations and, in the continuum limit, under diffeomorphisms. It is a theory that is well-behaved at small distances, and quantum fluctuations are well defined. We discuss how to check if Newton’s law is reproduced in the infrared limit in the world with fluctuating metrics. Our formulation of quantum gravity allows its unification with the Standard Model, and that will be also briefly discussed.

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Dr. Dmitri Diakonov, Petersburg Nuclear Physics Institute
Seminarraum Theoretische Physik
Contact: not specified