Abstract
As a first step in the construction of quantum field theories invariant under the group of diffeomorphisms, we obtain Fock space representations of the algebra of vector fields of the n-torus. These representations have the novel feature of being carried by bilinear forms rather than operators. Nevertheless all the usual manipulations can be defined via a suitable regularization procedure. Our approach is a generalization of Kac-Peterson’s method for Diff (S1) which allows us to explicitly construct “quantum fields” transforming as “classical” tensors.
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