Berezin Transforms Attached to Landau Levels on the Complex Projective Space Pn(ℂ)

Автор(и)

  • Nizar Demni Aix-Marseille Université CNRS Centrale Marseille I2M-UMR 7373. 39 rue F. Joliot Curie, 13453 Marseille, France
  • Zouhaïr Mouayn Department of Mathematics, Faculty of Sciences and Technics (M’Ghila), Sultan Moulay Slimane University, P.O. Box. 523, Béni Mellal, Morocco
    Department of Mathematics, KTH Royal Institute of Technology, SE-10044, Stockholm,Sweden
  • Houda Yaqine Department of Mathematics, Faculty of Sciences and Technics (M’Ghila), Sultan Moulay Slimane University, P.O. Box. 523, Béni Mellal, Morocco

DOI:

https://doi.org/10.15407/mag17.04.422

Ключові слова:

комплексний проєктивний простiр, когерентнi стани, перетворення Березiна, магнiтний лапласiан, лапласiан Фубiнi–Штудi, формула Курнвiндера, спiввiдношення Клебша–Ґордана, функцiя Кампе де Ферiє

Анотація

Ми будуємо когерентнi стани для кожного власного простору магнiтного лапласiана в комплексному проєктивному n-просторi для того, щоб застосувати метод квантизацiї-деквантизацiї. Це дозволяє визначити перетворення Березiна для цих просторiв. Потiм ми встановлюємо формулу для цього перетворення як функцiю вiд лапласiана Фубiнi–Штудi в замкненiй формi, яка мiстить кiнцеву функцiю Кампе де Ферiє. Для найнижчого сферичного рiвня Ландау на рiмановiй сферi одержана формула зводиться до формули одержаної самим Березiним. 

Mathematics Subject Classification: 81Q10, 47G10, 58C40, 46E22

Посилання

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Demni, N.; Mouayn, Z.; Yaqine, H. Berezin Transforms Attached to Landau Levels on the Complex Projective Space Pn(ℂ). Журн. мат. фіз. анал. геом. 2021, 17, 422-440.

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