Remarks on the geometric quantization of Landau levels

Mauro Spera, Andrea Galasso

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalInternational Journal of Geometric Methods in Modern Physics
Publication statusPublished - 2016


  • Landau levels
  • coherent states
  • geometric quantization
  • index theory
  • integrability
  • symplectic reduction


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