The Dressing Field Method of Gauge Symmetry Reduction: Presentation and Examples

Abstract

This paper is a presentation of a recent method of gauge symmetry reduction, distinct from the well-known gauge fixing, the bundle reduction theorem or even the Spontaneous Symmetry Breaking Mechanism (SSBM). Given a symmetry group G acting on a fiber bundle and its naturally associated fields (Ehresmann (or Cartan) connection, curvature, . . . ) there are situations where it is possible to erase (in whole or in part) the G-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 G (or a subgroup) does not act anymore. Two examples are presented in this paper: the re-interpretation of the BEGHHK (Higgs) mechanism without calling on a SSBM, and the top-down construction of Tractor and Twistor bundles and connections in the framework of conformal Cartan geometry.