论文标题
关于非交通空间中长度的量化
On the Quantization of Length in Noncommutative Spaces
论文作者
论文摘要
我们考虑具有直线坐标的规范/Weyl-subyal型非交通型（NC）空间。由量子机械谐波振荡与规范型NC 2-D空间的形式形式的类比进行类比的动机，并注意到后一种情况中长度的平方类似于前者的汉密尔顿人，我们得出的结论是，如果长度和区域在此类区域中量化，则该区域在该区域中量化，该区域是在该区域中的长度。我们将分析扩展到3-D病例，并制定阶梯操作员的方法，以量化3-D空间中的长度。但是，如果考虑到时和空间之间的非销量，我们的方法不适合1+1和2+1 Minkowski SpaceTime中的时空长度的量化。如果花时间与空间坐标进行通勤，并且仅在2+1和3+1维时时空中仅在空间坐标之间保持非交换性，则可以在我们的方法中进行空间长度的量化。
We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of the formalism of the quantum mechanical harmonic oscillator problem in quantum phase-space with that of the canonical-type NC 2-D space, and noting that the square of length in the latter case is analogous to the Hamiltonian in the former case, we arrive at the conclusion that the length and area are quantized in such an NC space, if the area is expressed entirely in terms of length. We extend our analysis to 3-D case and formulate a ladder operator approach to the quantization of length in 3-D space. However, our method does not lend itself to the quantization of spacetime length in 1+1 and 2+1 Minkowski spacetimes if the noncommutativity between time and space is considered. If time is taken to commute with spatial coordinates and the noncommutativity is maintained only among the spatial coordinates in 2+1 and 3+1 dimensional spacetime, then the quantization of spatial length is possible in our approach.
