Berezin Transforms Attached to Landau Levels on the Complex Projective Space Pn(ℂ)
DOI:
https://doi.org/10.15407/mag17.04.422Анотація
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
Ключові слова:
комплексний проєктивний простiр, когерентнi стани, перетворення Березiна, магнiтний лапласiан, лапласiан Фубiнi–Штудi, формула Курнвiндера, спiввiдношення Клебша–Ґордана, функцiя Кампе де ФерiєПосилання
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