论文标题
$ \ Mathbb {k} $ - 希尔伯特空间中的旋转器
Spinors in $\mathbb{K}$-Hilbert Spaces
论文作者
论文摘要
我们考虑$ \ mathbb {k} $ - Hilbert Space的结构，其中$ \ Mathbb {k} \ simeq \ simeq \ mathbb {r} $是一个实数的领域，$ \ mathbb {k} \ simeq \ mathbb {c} $是一个复杂数字，复杂的数字， $ \ Mathbb {K} \ simeq \ Mathbb {h} $是Clifford代数的框架内的Quaternion代数。 $ \ mathbb {k} $ - Hilbert Space由Gelfand-Naimark-Segal结构生成，而生成的$ C^\ AST $ -Algebra由Energy Operator $ h $和Group $ su SU（2,2）$的生成器组成。 $ \ mathbb {k} $ - 希尔伯特空间的循环矢量对应于Quaternionic代数的张量产物，定义了操作员代数的纯可分离状态。根据分区环$ \ mathbb {k} $，所有操作员代数的所有状态都分为三个类：1）用$ \ mathbb {k} \ simeq \ simeq \ mathbb {c} $; 2）具有$ \ mathbb {k} \ simeq \ mathbb {h} $的中性状态; 3）真正具有$ \ mathbb {k} \ simeq \ mathbb {r} $的中性状态。对于定义能量光谱的费米和骨状状态的纯可分离状态，确定融合，加倍（复合）和歼灭操作。
We consider a structure of the $\mathbb{K}$-Hilbert space, where $\mathbb{K}\simeq\mathbb{R}$ is a field of real numbers, $\mathbb{K}\simeq\mathbb{C}$ is a field of complex numbers, $\mathbb{K}\simeq\mathbb{H}$ is a quaternion algebra, within the framework of division rings of Clifford algebras. The $\mathbb{K}$-Hilbert space is generated by the Gelfand-Naimark-Segal construction, while the generating $C^\ast$-algebra consists of the energy operator $H$ and the generators of the group $SU(2,2)$ attached to $H$. The cyclic vectors of the $\mathbb{K}$-Hilbert space corresponding to the tensor products of quaternionic algebras define the pure separable states of the operator algebra. Depending on the division ring $\mathbb{K}$, all states of the operator algebra are divided into three classes: 1) charged states with $\mathbb{K}\simeq\mathbb{C}$; 2) neutral states with $\mathbb{K}\simeq\mathbb{H}$; 3) truly neutral states with $\mathbb{K}\simeq\mathbb{R}$. For pure separable states that define the fermionic and bosonic states of the energy spectrum, the fusion, doubling (complexification) and annihilation operations are determined.
