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. Mathematics Subject Classification (2010). Primary 99Z99; Secondary 00A00.
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Jeremy Attard. The Dressing Field Method of Gauge Symmetry Reduction: Presentation and Examples. Geometric Methods in Physics XXXVI: Workshop and Summer School, Białowieża, Poland, 2017, pp.199-205, 2019, Trends in Mathematics, 9783030011567. ⟨10.1007/978-3-030-01156-7_21⟩. ⟨hal-02071455⟩



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