Scope and goal

The main goal of this workshop was to bring together scientists working in noncommutative geometry and in particle physics, to see how experimental findings (e.g. in particle accelerators, but not exclusively) provide inspiration for noncommutative geometry, and vice versa, how noncommutative geometry can provide tools for phenomenological model-building.

 

Development

The workshop consisted of morning lectures (crash courses) on topics in noncommutative geometry for particle physicists (by Alain Connes, Walter van Suijlekom and Ali Chamseddine) and vice versa on particle physics for noncommutative geometers (by Elisabetta Pallante). Also, on Monday experimental updates were given on dark matter searches and on particle searches at the LHC, and a Higgs status report (Patrick Decowski, Paul de Jong and Stan Bentvelsen); which already on the first day led to lively discussions. Here it became clear that noncommutative geometry and experiments in particle physics both take a spectral point of view in analyzing the fine-structure of spacetime and matter: in the first through the spectrum of a linear operator, in the second through the energy spectrum.

 

Besides more advanced seminars there was much discussion time during the workshop, in particular through the "study groups". In the latter, two topics were selected (out of four) by the participants: Higgs vacuum stability and Lorentzian NCG: is space-time non-commutative? After the breakout in two groups, a plenary discussion brought thoughts and new insights together. Also, the discussions were sustained by a website noncommutativegeometry.nl, serving as a repository with background material

as well.

 

Beyond the workshop

One of the successes of the workshop was that the mingling between noncommutative geometers and particle physicists actually took place, which is not an automatic result. In this respect, the active attitude of the latter in critically evaluating the noncommutative approach was very valuable. On Friday, it eventually led to new research questions during the final discussion which, though still open, could be formulated with clarity. This naturally suggests directions for future research in noncommutative model-building and in making predictions for physics beyond the Standard Model.

 

Acknowledgement

The organizational support of the Lorentz Center was excellent, leaving essentially only research problems for the organizers. Also the open nature of the facility at Snellius was greatly appreciated by all participants.

 

 

Thijs van den Broek. Radboud University Nijmegen.

Alain Connes. Collège de France. Institut des Hautes Études Scientifiques

José Gracia-Bondía. Universidad de Zaragoza.

Piet Mulders. Vrije Universiteit Amsterdam.

Walter D. van Suijlekom. Radboud University Nijmegen.