论文标题
没有本征代代数或张量产物的物理空间中的Spin-1/2一单粒子系统和两种粒子系统
Spin-1/2 one- and two- particle systems in physical space without eigen-algebra or tensor product
论文作者
论文摘要
在自旋位置解耦近似下，具有几何代数的3D方向空间中具有相位相位的向量，取代了构建在Pauli Spin Operator上的矢量 - 矩阵旋转模型。标准的量子算子态旋转形式主义被矢量取代，矢量是在相同的3D空间中旋转的适当和不当旋转的 - 同构对Pauli矩阵的空间。在单个旋转案例中，小说旋转1/2表示：（1）是Hermitian； （2）显示惯用性； （3）产生所有标准结果，其模量等于总自旋角动量S_TOT； （4）正式的测量中的不可逆性； （5）允许在3D中自适应嵌入2D自旋空间。最大纠缠的自旋对：（1）处于相位，并且具有相反的手。 （2）与3D中的四个基本不当旋转之一相关联：三胞胎的平面反射和单元的反转； （3）产生标准的总角动量； （4）随后是两分和部分观察的所有标准期望值。根据正确和不当转子的行为是一两个方面的作用，形式主义分别以两种互补形式出现，分别是旋转器或矢量形式。所提出的方案提供了完全在3D物理方向空间中的自旋相关和转换的清晰几何图片。
Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state spin formalism is replaced with vectors transforming by proper and improper rotations in the same 3D space -- isomorphic to the space of Pauli matrices. In the single spin case the novel spin 1/2 representation: (1) is Hermitian; (2) shows handedness; (3) yields all the standard results and its modulus equals the total spin angular momentum S_tot; (4) formalizes irreversibility in measurement; (5) permits adaptive embedding of the 2D spin space in 3D. Maximally entangled spin pairs: (1) are in phase and have opposite handedness; (2) relate by one of the four basic improper rotations in 3D: plane-reflections for triplets and inversion for singlet; (3) yield the standard total angular momentum; (4) all standard expectation values for bipartite and partial observations follow. Depending on whether proper and improper rotors act one or two sided, the formalism appears in two complementary forms, the spinor or the vector form, respectively. The proposed scheme provides a clear geometric picture of spin correlations and transformations entirely in the 3D physical orientation space.
