Berlin 2015 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 6: Quantenfeldtheorie I

MP 6.2: Talk

Wednesday, March 18, 2015, 09:50–10:10, HFT-FT 101

The BV formalism for the BRST quantization of matrix models: a noncommutative geometric approach. — •Roberta A. Iseppi — Radboud University, Nijmegen, The Netherlands

In recent years noncommutative geometry has given proof of being an interesting mathematical framework to describe gauge theories: the strong connection between noncommutative geometry and gauge theories lies in the fact that gauge theories are naturally induced by spectral triples, which are the main technical device in contemporary noncommutative geometry. It is then reasonable to try to insert in the setting of noncommutative geometry also procedures which have been developed for the analysis of gauge theories. One of these is the BV approach to the BRST quantization of non-abelian gauge theories.

We present a method to incorporate this approach in the framework of noncommutative geometry. We restrict to a U(2)-gauge invariant matrix model: through the introduction of a so-called BV-spectral triple we describe the minimally-extended theory, obtained by inserting the minimal number of ghost fields. An interesting aspect of this approach is that it gives a “geometric interpretation” for all the physical properties of the ghost fields such as their bosonic or fermionic character, which have a natural translation in terms of the spectral triple itself.