This is mainly a review of an intense 15-year long collaboration between the authors on explicit realisations of compact Lie groups and their applications. Starting with an elementary example, we will illustrate the main idea at the foundation of the generalisation of the Euler parametrisation of SU(2) to any compact Lie group. Based on this, we will provide a very detailed reconstruction of the possible Euler parametrisation associated with the so-called symmetric embedding. Then, we will recall how such constructions are related to the Dyson integrals, providing a geometrical interpretation of the latter, at least in certain cases. This includes a short review on the main properties of simple Lie groups, algebras, and their representations. Finally, we will conclude with some applications to nuclear physics and to measure theory in infinite dimensions and discuss some open questions.

Compact Lie Groups, Generalised Euler Angles, and Applications

Sergio Luigi Cacciatori;
2022-01-01

Abstract

This is mainly a review of an intense 15-year long collaboration between the authors on explicit realisations of compact Lie groups and their applications. Starting with an elementary example, we will illustrate the main idea at the foundation of the generalisation of the Euler parametrisation of SU(2) to any compact Lie group. Based on this, we will provide a very detailed reconstruction of the possible Euler parametrisation associated with the so-called symmetric embedding. Then, we will recall how such constructions are related to the Dyson integrals, providing a geometrical interpretation of the latter, at least in certain cases. This includes a short review on the main properties of simple Lie groups, algebras, and their representations. Finally, we will conclude with some applications to nuclear physics and to measure theory in infinite dimensions and discuss some open questions.
https://www.mdpi.com/2218-1997/8/10/492
Lie groups; Euler angles; representations; Dyson integrals; symmetric spaces
Cacciatori, SERGIO LUIGI; Scotti, Antonio
File in questo prodotto:
File Dimensione Formato  
me-universe I-2-2022.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 573.86 kB
Formato Adobe PDF
573.86 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2143955
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact