论文标题
操作员说明旋转和变换的代数
Operator Lie Algebras of Rotations and Transformations in White Noise
论文作者
论文摘要
与复杂的Gelfand Triple $相关的无限尺寸旋转组的一参数亚组的无限发电机 （e）\ subset l^2（e^*，μ）\ subset（e）^* $ 是$$r_κ=的形式 \ int_ {t \ times t}κ（s，t）（a_s^* a_t -a_t^* a_s）ds ds ds dt $$其中$κ\在e \ otimes e^* $中是一个偏斜的分布。因此，$r_κ$是与偏斜的操作员$ s $相关的保护操作员的两倍。讨论了包含$r_κ$，身份操作员，歼灭操作员，创建操作员，数字操作员，（广义）laplacian的谎言代数。我们表明，这个谎言代数与偏斜的操作员$ S $的轨道相关。
The infinitesimal generator of a one-parameter subgroup of the infinite dimensional rotation group associated with the complex Gelfand triple $ (E) \subset L^2(E^*, μ) \subset (E)^* $ is of the form $$ R_κ= \int_{T\times T} κ(s,t) (a_s^* a_t - a_t^* a_s) ds dt $$ where $κ\in E \otimes E^*$ is a skew-symmetric distribution. Hence $R_κ$ is twice the conservation operator associated with a skew-symmetric operator $S$. The Lie algebra containing $R_κ$, identity operator, annihilation operator, creation operator, number operator, (generalized) Gross Laplacian is discussed. We show that this Lie algebra is associated with the orbit of the skew-symmetric operator $S$.
