AI 中文总结
本研究分析了多电子狄拉克-库仑哈密顿量中用于诊断克拉默斯污染的守恒量构造，确定其对应赝自旋分量，指出所提量子数的对易关系不成立，该量子数无效。
AI 中文摘要
已有研究提出，多电子狄拉克-库仑哈密顿量中单电子时间反演之和的平方是具有整数本征值谱的守恒量[Phys. Rev. A 94, 052104 (2016)]，其期望值被用作克拉默斯污染的诊断指标。本研究确定了该构造背后的算符，即附加于所选克拉默斯对的赝自旋的一个分量，其角动量代数可重现已报道的谱并以闭式形式给出本征向量。所提量子数$-k^2$中的标记$k$是赝自旋在基固定轴上投影幅度的两倍，且当克拉默斯对重新定相时会发生变化。该算符与哈密顿量的对易关系不成立，所提量子数不成立。
英文摘要
The square of a sum of single-electron time reversals has been proposed as a conserved quantity with an integer eigenvalue spectrum for the many-electron Dirac-Coulomb Hamiltonian [Phys. Rev. A 94, 052104 (2016)], and its expectation value is in use as a diagnostic of Kramers contamination. This work identifies the operator behind the construction, a component of a pseudospin attached to the chosen Kramers pairs, whose angular-momentum algebra reproduces the reported spectrum and yields the eigenvectors in closed form. The label $k$ entering the proposed quantum number $-k^2$ is twice the magnitude of a pseudospin projection onto an axis fixed by the basis and changes when the Kramers pairs are rephased. The commutation with the Hamiltonian is unfounded, and the proposed quantum number does not stand.
Comments21 pages
