Transformations de Bargmann Discrètes Attachées aux Niveaux de Landau sur la Sphère de Riemann

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• 作者：Zouha?r Mouayn
• 刊名：Annales Henri Poincare
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：16
• 期：2
• 页码：641-650
• 全文大小：228 KB
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• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Dynamical Systems and Ergodic Theory
  Quantum Physics
  Mathematical Methods in Physics
  Relativity and Cosmology
  Elementary Particles and Quantum Field Theory
  
• 出版者：Birkh盲user Basel
• ISSN：1424-0661

文摘

We construct a family of transforms labeled by (ν, m) and mapping isometrically square integrable functions on a finite subset of \({\mathbb{R}}\) onto L 2-eigenspaces associated with the discrete spectrum of a charged particle evolving in the Riemann sphere under influence of a uniform magnetic field with a strength proportional to \({2\nu \in \mathbb{Z}_{+}^{\ast}}\) . These transforms are attached to spherical Landau levels \({\lambda _{m}^{\nu}=\left( 2m+1\right) \nu +m\left( m+1\right)}\) with \({m\in \mathbb{Z}_{+}}\) and are called discrete Bargmann transforms.