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Relativistic gauge theories and non-commutative geometry

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I explain how the representation theory of loop groups provides mathematical tools to construct QCD , i.e. QCD in 1+1 space-time dimensions with massless fermions. I describe mathematical results on corresponding higher dimensional analogues of the loop groups that are motivated by QCD . I explain why I believe that ideas from non-commutative geometry (NCG) should be useful to get a better mathematical understanding of QCD beyond perturbation theory.

One particular aspect of NCG was popularized by Seiberg and Witten in 1999 in particle physics – I thus should stress that I mean NCG in a much broader sense than this.

Comments: I plan to revisit and review a research topic I worked on until 2001.

My talk will be based on my papers from that time, including

-EL and G.W. Semenoff, QCD with massless quarks and gauge covariant Sugawara construction, Phys. Lett. B 341 (1994) 195

-EL and J. Mickelsson, (3+1)-dimensional Schwinger terms and non-commutative geometry, Phys. Lett. B 338 (1994) 241

-EL, Quantum gauge theories and non-commutative geometry, arXiv:hep-th/9608003 etc.

This talk is part of the Isaac Newton Institute Seminar Series series.

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