磁叶上so(2, 2k+2)的泊松实现
数学物理
2015-06-12 v5 math.MP
辛几何
摘要
令 R ∗ 2 k + 1 = R 2 k + 1 ∖ { 0 ⃗ } {\mathbb R}^{2k+1}_*={\mathbb R}^{2k+1}\setminus\{\vec 0\} R ∗ 2 k + 1 = R 2 k + 1 ∖ { 0 } k ≥ 1 k\ge 1 k ≥ 1 π \pi π R ∗ 2 k + 1 → S 2 k {\mathbb R}^{2k+1}_*\to \mathrm{S}^{2k} R ∗ 2 k + 1 → S 2 k r ⃗ ∈ R ∗ 2 k + 1 \vec r\in {\mathbb R}^{2k+1}_* r ∈ R ∗ 2 k + 1 r ⃗ ∣ r ⃗ ∣ ∈ S 2 k {\vec r\over |\vec r|}\in \mathrm{S}^{2k} ∣ r ∣ r ∈ S 2 k P → R ∗ 2 k + 1 P\to {\mathbb R}^{2k+1}_* P → R ∗ 2 k + 1 π \pi π S O ( 2 k ) \mathrm{SO}(2k) SO ( 2 k ) S O ( 2 k + 1 ) → S 2 k \mathrm{SO}(2k+1)\to \mathrm{S}^{2k} SO ( 2 k + 1 ) → S 2 k E ♯ → R ∗ 2 k + 1 E_\sharp\to {\mathbb R}^{2k+1}_* E ♯ → R ∗ 2 k + 1 E ♯ → T ∗ R ∗ 2 k + 1 E^\sharp\to T^*{\mathbb R}^{2k+1}_* E ♯ → T ∗ R ∗ 2 k + 1 T ∗ R ∗ 2 k + 1 → R ∗ 2 k + 1 T^*{\mathbb R}^{2k+1}_*\to {\mathbb R}^{2k+1}_* T ∗ R ∗ 2 k + 1 → R ∗ 2 k + 1 S O ( 2 k + 1 ) → S 2 k \mathrm{SO}(2k+1)\to \mathrm{S}^{2k} SO ( 2 k + 1 ) → S 2 k E ♯ E^\sharp E ♯ s o ( 2 , 2 k + 2 ) \mathfrak{so}(2, 2k+2) so ( 2 , 2 k + 2 ) ( C ∞ ( O ♯ ) , { , } ) (C^\infty(\mathcal O^\sharp), \{, \}) ( C ∞ ( O ♯ ) , { , }) O ♯ \mathcal O^\sharp O ♯ E ♯ E^\sharp E ♯ 2 k + 1 2k+1 2 k + 1
引用
@article{arxiv.1211.5992,
title = {The Poisson Realization of so(2, 2k+2) on Magnetic Leaves},
author = {Guowu Meng},
journal= {arXiv preprint arXiv:1211.5992},
year = {2015}
}
备注
14 pages