论文标题
张量旋转的表示和自旋1/2的几何形状
Representations of tensor rotations and the geometry of spin 1/2
论文作者
论文摘要
利用真实的SL（2，r）谎言组代数生成自旋1/2谎言组，可以创建一个明确给定的洛伦兹不变的费米恩波。由于发电机是真正的价值，它们可以被解释为变形张量，尤其是空间的变形张量。因此，有可能在Minkowski空间中对自旋1/2的启发式纯粹几何表示进行建模。但是，更大的惊喜是，该波具有引力波的时空结构，这被理解为自旋2波。鉴于角动量表示的唯一性仍然存在，因此张量旋转的检查揭示了由于对称张量的未计算的基本对称性，具有不同角参数的张量旋转的不同表示，其中自旋1/2表示对应于量子量量量的特定表示。看起来矛盾已经完全解决，除了了解张量中自旋的不同表示的概念外，再次与张量的不同表示有关。
Making use of the real sl(2,R) Lie group algebra generating a spin 1/2 Lie group allows to create an explicitly given Lorentz invariant fermion wave. As the generators are real valued they can be interpreted as a deformation tensor in particular as a deformation tensor of space. Therefore, it is possible to model a heuristic purely geometric representation of spin 1/2 in Minkowski space. However the bigger surprise is that this wave has the space-time structure of gravitational waves, which are understood to be spin 2 waves. Given that the uniqueness of angular momentum representations still holds, the examination of tensor rotations reveals the existence of different representations of tensor rotations with a different angular parameter due to an unaccounted basic symmetry of symmetric tensors, where the spin 1/2 representation is a specific representation of tensor rotations corresponding to the quantum theoretical approach. The seeming contradiction is fully resolved and allows in addition to understand the notion of different representations of spin in tensors, again related to different representations of the tensor.
