Abstract Let k ≥ 1 be an integer and μ be the half of a nonzero integer. It is reported here that the phase space of the ( 2 k + 1 ) -dimensional magnetized Kepler problem with magnetic charge μ can be identified with the elliptic co-adjoint orbit of the real Lie algebra so ( 2 , 2 k + 2 ) that corresponds to the dominant weight ( | μ | , … , | μ | ︸ k + 1 , μ ) . As a corollary, one has the following result: the aforementioned elliptic co-adjoint orbit admits a natural quantization in which the Hilbert space of quantum states is the space of square integrable sections of a Hermitian vector bundle over the punctured Euclidean space in dimension 2 k + 1 ; moreover, this Hilbert space provides a geometric realization for the unitary highest weight so ( 2 , 2 k + 2 ) -module with highest weight ( − k − | μ | , | μ | , … , | μ | ︸ k , μ ) .

中文翻译：

---

磁化开普勒流形及其量化

摘要 设 k ≥ 1 为整数，μ 为非零整数的一半。这里报道了( 2 k + 1 )维磁化开普勒问题的相空间与磁荷μ可以用实李代数的椭圆共伴随轨道识别，所以 ( 2 , 2 k + 2 )对应于主导权重 (| μ | , … , | μ | ︸ k + 1 , μ ) 。作为推论，有以下结果：上述椭圆共伴轨道允许自然量子化，其中量子态的希尔伯特空间是 2 k 维穿孔欧几里得空间上厄米向量丛的方形可积部分的空间+ 1 ; 此外，该希尔伯特空间为具有最高权重 ( − k − | μ | , | μ | , … , | μ | ︸ k , μ ) 的幺正最高权重 so ( 2 , 2 k + 2 ) 模块提供了几何实现.