In this note, we resume the geometric quantization approach to the motion of a charged particle on a plane, subject to a constant magnetic field perpendicular to the latter, by showing directly that it gives rise to a completely integrable system to which we may apply holomorphic geometric quantization. In addition, we present a variant employing a suitable vertical polarization and we also make contact with Bott’s quantization, enforcing the property “quantization commutes with reduction”, which is known to hold under quite general conditions. We also provide an interpretation of translational symmetry breaking in terms of coherent states and index theory. Finally, we give a representation theoretic description of the lowest Landau level via theuse of an S^1-equivariant Dirac operator.

Galasso, A., Spera, M., Remarks on the geometric quantization of Landau levels, <<INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS>>, 2016; 2016 (10): 1-19 [http://hdl.handle.net/10807/86564]

Remarks on the geometric quantization of Landau levels

Spera, Mauro
2016

Abstract

In this note, we resume the geometric quantization approach to the motion of a charged particle on a plane, subject to a constant magnetic field perpendicular to the latter, by showing directly that it gives rise to a completely integrable system to which we may apply holomorphic geometric quantization. In addition, we present a variant employing a suitable vertical polarization and we also make contact with Bott’s quantization, enforcing the property “quantization commutes with reduction”, which is known to hold under quite general conditions. We also provide an interpretation of translational symmetry breaking in terms of coherent states and index theory. Finally, we give a representation theoretic description of the lowest Landau level via theuse of an S^1-equivariant Dirac operator.
eng
Galasso, A., Spera, M., Remarks on the geometric quantization of Landau levels, <>, 2016; 2016 (10): 1-19 [http://hdl.handle.net/10807/86564]
File in questo prodotto:
File Dimensione Formato  
Galasso-Spera-IJGMMP-VQR.pdf

non disponibili

Tipologia file ?: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 290.64 kB
Formato Unknown
290.64 kB Unknown   Visualizza/Apri   Contatta l'autore

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: http://hdl.handle.net/10807/86564
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact