The theory of Feynman diagrams is motivated by atomic physics and is standard material in the quantum field theory class. Example: Peskin and Schroeder talk about a spinor valued field over real or Lorentzian 4-space. These lead to badly divergent series and creative regularization methods.
I have a question what the Jones polynomials has to do with von Neumann algebras?

*[See the answers to https://mathoverflow.net/questions/97788/on-connection-between-knot-theory-and-operator-algebra -T.]*

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