XXXVI Workshop on Geometric Methods in Physics 2-8.07.2017
VI School on Geometry and Physics 26-30.06.2017

Jeremy Attard

The dressing field method of gauge symmetry reduction : presentation and examples.

This talk is a presentation of a recent method of gauge symmetry reduction, distinct from well-known gauge fixing, bundle reduction theorem or even spontaneous symmetry breaking mechanism (SSBM). Given a symmetry group H acting on a fiber bundle and its naturally associated fields (Ehresmann (or Cartan) connection, curvature, …) there sometimes exists a way to erase (in whole or in part) the H-action by just reconfiguring these fields, i.e. by making a mere change of field variables in order to get new (« composite ») fields on which H (in whole or in part) does not act anymore. Two examples : the re-interpretation of the BEHGHK (Higgs) mechanism without calling on a SSBM, and the top-down construction of Tractor and Twistor spaces and connections in the framework of conformal Cartan geometry, will be outlined at the end of the talk.

*arXiv:1001.1176 (about Higgs mechanism);
*arXiv:1212.6702 (the method + examples);
*arXiv:1512.06907 (dressing method and Weyl gravity);
*arXiv:1611.03891 and arXiv:1609.07307 (Tractors and Twistors).

Event sponsored by:
Centre de recherches mathématiques          University
of Bialystok
University of Bialystok

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