Measures on Hilbert-Schmidt operators and algebraic quantum field theory

Abstract

We present a general construction of non-Gaussian probability measures on the space of distributional kernels obeying a natural extension of the Osterwalder-Schrader axioms of Euclidean quantum field theory in arbitrary space-time dimension $d$. These measures may be interpreted as corresponding to scalar massive quantum fields with polynomial self-interaction. As a consequence, we obtain examples of non-free models satisfying the Haag-Kastler axioms of algebraic quantum field theory for arbitrary $d$. When $d<4$ we are able to transfer the measures to the space of distributions and verify the standard Osterwalder-Schrader axioms, hence, by a well-known reconstruction theorem, we also obtain quantum field theory models satisfying the axioms of Wightman.

arXiv commentThis paper has been withdrawn due to an error in the main construction. See arXiv:1701.05569 for a related result