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Positive TQFT

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Category theory; homological algebra; Quantum theory; Algebraic structures

video/mp4

Author affiliation: Universidad Nacional Autónoma de México

2017-02-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60586

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/