The dressing field method of gauge symmetry reduction, a review with examples

Abstract

Gauge symmetries are a cornerstone of modern physics but they come with technical difficulties when it comes to quantization, to accurately describe particles phenomenology or to extract observables in general. These shortcomings must be met by essentially finding a way to effectively reduce gauge symmetries. We propose a review of a way to do so which we call the dressing field method. We show how the BRST algebra satisfied by gauge fields, encoding their gauge transformations, is modified. We outline noticeable applications of the method, such as the electroweak sector of the Standard Model and the local twistors of Penrose.

arXiv commentSubmitted to International Journal of Geometric Methods in Modern Physics, 38 pages. arXiv admin note: text overlap with arXiv:1611.03891, arXiv:1609.07307

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• Holism as the significance of gauge symmetries
• Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method
• Dressing vs. Fixing: On How to Extract and Interpret Gauge-Invariant Content
• The Fröhlich-Morchio-Strocchi mechanism and quantum gravity
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• Dilaton from Tractor and Matter Field from Twistor
• Relational Supersymmetry via the Dressing Field Method and Matter-Interaction Supergeometric Framework
• The Fröhlich-Morchio-Strocchi mechanism: A underestimated legacy