Is a topological quantum field theory metrizable? or else a tqft coming from a subfactor?
For a given metric, are there always renormalization and Feynman diagrams?
Is there always a Feynman motive related to it?
Finally, does this Feynman motive depend on the choice of the metric?
Clarification by the OP given in a comment here
"First, all these questions could be unified by "Is the Feynman motive a topological invariant?". My motivation comes from the observation that the subfactors theory and the motives theory are both an "enriched Galois theory" so that I asked myself if there is a link between these two enrichment. The path through TQFTs and Feynman motives could be a link."
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- Connes, Kreimer; Renormalization in quantum field theory and the Riemann-Hilbert problem I and II; 2000, 2001.
- Connes, Marcolli; Noncommutative Geometry, Quantum Field Theory and Motives; 2008.
- Henry; From toposes to non-commutative geometry through the study of internal Hilbert spaces; PhD dissertation; 2014.
- Kodiyalam, Sunder; Topological quantum field theories from subfactors; 2000.
- Kodiyalam, Sunder, Vishwambhar; Subfactors and 1+1-dimensional TQFTs; 2005.
- Marcolli; Feynman motives; 2010.
This post imported from StackExchange Physics at 2014-10-06 20:59 (UTC), posted by SE-user Sébastien Palcoux