The dressing field method in gauge theories - geometric approach

Marcin Zając; Marcin Zając

doi:10.3934/jgm.2023007

Journal of Geometric Mechanics

2023, Volume 15, Issue 1: 128-146. doi: 10.3934/jgm.2023007

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Research article

The dressing field method in gauge theories - geometric approach

Marcin Zając ^,

Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland

Received: 14 May 2021 Revised: 19 September 2022 Accepted: 26 September 2022 Published: 29 January 2023
Primary: 53Z05; Secondary: 70S05, 70S10, 70S15

Recently, T. Masson, J. Francois, S. Lazzarini, C. Fournel and J. Attard have introduced a new method of the reduction of gauge symmetries called the dressing field method. In this paper we analyse this method from the fiber bundle point of view and we show the geometric implications for a principal bundle underlying a given gauge theory.We show how the existence of a dressing field satisfying certain conditions naturally leads to the reduction of the principal bundle and, as a consequence, to the reduction of the configuration and phase bundle of the system.
- dressing field method,
- gauge theories,
- jet bundles,
- principal bundles,
- reduction
Citation: Marcin Zając. The dressing field method in gauge theories - geometric approach[J]. Journal of Geometric Mechanics, 2023, 15(1): 128-146. doi: 10.3934/jgm.2023007

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Abstract

Recently, T. Masson, J. Francois, S. Lazzarini, C. Fournel and J. Attard have introduced a new method of the reduction of gauge symmetries called the dressing field method. In this paper we analyse this method from the fiber bundle point of view and we show the geometric implications for a principal bundle underlying a given gauge theory.We show how the existence of a dressing field satisfying certain conditions naturally leads to the reduction of the principal bundle and, as a consequence, to the reduction of the configuration and phase bundle of the system.

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