论文标题
高空空间费米，莫比乌斯的变换，凯林空间，费米昂加倍，暗物质
Hyperspace fermions,Möbius transformations, Krein space, fermion doubling, dark matter
论文作者
论文摘要
我们开发了一种经典和量子力学的方法，在该方法中，无限参数$ t $延长了连续时间，并将运动方程转换为差异方程。这些方程式得到解决，然后采用物理极限$ t \ rightarrow 0 $。原则上，该策略应将所有标准解决方案恢复到原始连续时间微分方程。我们发现这对于玻感变量是有效的，而随着费米的，发生了其他解决方案。对于玻色子和费米子，运动的差异方程可能与投射几何形状中的Möbius变换有关。通过Schwinger的作用原理进行量化可恢复玻色子的标准粒子 - 抗粒子模式，但在fermions的情况下，希尔伯特空间必须用凯林空间代替。我们讨论了与费米昂加倍问题和暗物质的可能联系。
We develop an approach to classical and quantum mechanics where continuous time is extended by an infinitesimal parameter $T$ and equations of motion converted into difference equations. These equations are solved and the physical limit $T \rightarrow 0$ then taken. In principle this strategy should recover all standard solutions to the original continuous time differential equations. We find this is valid for bosonic variables whereas with fermions, additional solutions occur. For both bosons and fermions, the difference equations of motion can be related to Möbius transformations in projective geometry. Quantization via Schwinger's action principle recovers standard particle-antiparticle modes for bosons but in the case of fermions, Hilbert space has to be replaced by Krein space. We discuss possible links with the fermion doubling problem and with dark matter.
