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Positive TQFT Oeckl, Robert


I discuss a class of topological quantum field theories that I call "positive TQFTs". In these the objects associated to hypersurfaces are partially ordered vector spaces and the morphisms associated to cobordisms are completely positive linear maps. I describe a functorial construction that coverts "ordinary" TQFTs into positive TQFTs by "taking the modulus square". The mathematical exploration of positive TQFTs is wide open. Physically, positive TQFTs arise from an operational description of both classical statistical field theory and quantum statistical field theory. There, the "modulus square" construction converts a quantum field theory in the sense of Segal into a mixed state counterpart. The latter is of interest for the foundations of quantum theory and for quantum gravity.

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