论文标题
量子力学的三个空间
Three-space from quantum mechanics
论文作者
论文摘要
Penrose的自旋几何定理从$ SU（2）$（3）$（3）$（Euclidean）不变基本量子机械系统。将总角动量自然分解为其自旋和轨道部位，可以从\ emph {相对轨道角动量}中恢复经典复合系统的基本子系统的质量质量}，由$ e（3）$ - $ e（3）$ - $ - $ - 3）$ - $ - $ - $ - 3）$ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - n e emph {3）。由这个观察结果激励，是\ emph {复合量子机械系统的基本子系统之间的“经验距离”的表达，建议用$ e（3）$ - 不变的量子观测值给出。结果表明，在经典的限制中，该表达式重现了子系统之间的\ emph {先验的欧几里得距离，尽管在量子级别上，它具有离散的字符。还考虑了“经验”角度和3卷元素。
The spin geometry theorem of Penrose is extended from $SU(2)$ to $E(3)$ (Euclidean) invariant elementary quantum mechanical systems. Using the natural decomposition of the total angular momentum into its spin and orbital parts, the \emph{distance} between the centre-of-mass lines of the elementary subsystems of a classical composite system can be recovered from their \emph{relative orbital angular momenta} by $E(3)$-invariant classical observables. Motivated by this observation, an expression for the `empirical distance' between the elementary subsystems of a \emph{composite quantum mechanical system}, given in terms of $E(3)$-invariant quantum observables, is suggested. It is shown that, in the classical limit, this expression reproduces the \emph{a priori} Euclidean distance between the subsystems, though at the quantum level it has a discrete character. `Empirical' angles and 3-volume elements are also considered.
