论文标题
离散的相空间和连续的相对论量子力学I：Planck振荡器和闭合的弦圆形轨道
Discrete phase space and continuous time relativistic quantum mechanics I: Planck oscillators and closed string-like circular orbits
论文作者
论文摘要
研究了涉及特征长度$ l $的相对论量子力学的离散相空间连续时间表示。纸张的大多数部分都保留了基本的物理常数，例如$ \ hbar $，$ c $和$ l $。 Planck振荡器的能量特征值问题在此框架中精确解决。在离散（1 + 1）-Dimensional Phase平面中，恒定能量的离散偶发轨道被证明是圆圈$ s^{1} _ {n} $。此外，这些轨道的时间演变像几何实体一样扫除世界表$ s^{1} _ {n} \ times \ times \ mathbb {r} \ subset \ subset \ subset \ mathbb {r}^2 $，因此如封闭的字符串样构型配置。这些离散轨道在相位空间中的物理解释以数学上的严格方式显示为退化，类似弦的相位细胞。这些封闭的绕节轨道在离散相空间量子力学的舞台上的存在，该机制以低阶膨胀的非单明性性质而闻名，$ s^{\＃} $矩阵项已知存在，但直到现在尚未得到充分探索。最后，在连续不均匀的正交组$ \ MATHCAL {i} [o（3,1）] $下，离散的部分差异差异klein-gordon方程显示为不变。
The discrete phase space continuous time representation of relativistic quantum mechanics involving a characteristic length $l$ is investigated. Fundamental physical constants such as $\hbar$, $c$, and $l$ are retained for most sections of the paper. The energy eigenvalue problem for the Planck oscillator is solved exactly in this framework. Discrete concircular orbits of constant energy are shown to be circles $S^{1}_{n}$ of radii $2E_n =\sqrt{2n+1}$ within the discrete (1 + 1)-dimensional phase plane. Moreover, the time evolution of these orbits sweep out world-sheet like geometrical entities $S^{1}_{n} \times \mathbb{R} \subset \mathbb{R}^2$ and therefore appear as closed string-like geometrical configurations. The physical interpretation for these discrete orbits in phase space as degenerate, string-like phase cells is shown in a mathematically rigorous way. The existence of these closed concircular orbits in the arena of discrete phase space quantum mechanics, known for the non-singular nature of lower order expansion $S^{\#}$ matrix terms, was known to exist but has not been fully explored until now. Finally, the discrete partial difference-differential Klein-Gordon equation is shown to be invariant under the continuous inhomogeneous orthogonal group $\mathcal{I} [O(3,1)]$ .
