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

Jérémy Attard (1, 2) , J. François (3) , S. Lazzarini (1, 2) , T. Masson (2, 1)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 7332
3 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: Gauge field theories; tractors; conformal geometry; BRST algebra; 1125Hf; numbers: 0240Hw; symmetry reduction; electroweak theory; Cartan geometry; 1115-q; Dressing Field Method; twistors

Domaines: Physique mathématique [math-ph]; Relativité Générale et Cosmologie Quantique [gr-qc]; Géométrie différentielle [math.DG]

Jérémy Attard, J. François, S. Lazzarini, T. Masson. The dressing field method of gauge symmetry reduction, a review with examples. Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives, Springer, pp.377-415, 2018, 978-3-319-64812-5. ⟨10.1007/978-3-319-64813-2⟩. ⟨hal-01464130⟩