Aug. 21 Math Phys 
14:00  15:30 RIMS 110 
Gábor Etesi (UIUC)
Gravity as a four dimensional algebraic quantum field theory
Based on an indefinite unitary representation of the diffeomorphism group of an oriented 4manifold an algebraic quantum field theory formulation of gravity is exhibited. More precisely the representation space is a Krein space therefore as a vector space it admits a family of direct sum decompositions into orthogonal pairs of maximal definite Hilbert subspaces coming from the Krein space structure. It is observed that the C*algebra of bounded linear operators associated to this representation space contains algebraic curvature tensors. Classical vacuum gravitational fields i.e., Einstein manifolds correspond to quantum observables obeying at least one of the above decompositions of the space. In this way classical general relativity exactly in 4 dimensions naturally embeds into an algebraic quantum field theory whose net of local C*algebras is generated by local algebraic curvature tensors and vector fields. This theory is constructed out of the structures provided by an oriented 4manifold only, and hence possesses a diffeomorphism group symmetry. Motivated by the GelfandNaimarkSegal construction and the DouganMason construction of quasilocal energymomentum we construct certain representations of the limiting global C*algebra what we call the "positive mass representations". Finally we observe that the bunch of these representations give rise to a 2 dimensional conformal field theory in the sense of G. Segal.
