论文标题
Bogolyubov转换的Fock空间表示形式作为自旋表示
Fock space representations of Bogolyubov transformations as spin representations
论文作者
论文摘要
Bogolyubov转换组的Fock空间上的表示形式被认为是正交组的自旋表示。基于对两个Bogolyubov Quasi-Fermion真空状态的重叠幅度的某些已知公式的衍生结果，在某些情况下比文献中更完整。可以指出的是，文献中将“ Onishi公式”的名称分配给了两个不同的表达式，这些表达式相关但具有不同的范围。其中一个具有被描述为标志性问题的东西，另一个由于Onishi和Yoshida，其范围更有限，没有标志问题。我简短地证明了后者的简短证明，在Onishi和Yoshida的论文中缺少其派生，以及一个新的，组合的证明Robledo最近得出的等效公式。
The representation on a Fock space of the group of Bogolyubov transformations is recognized as the spin representation of an orthogonal group. Derivations based on this observation of some known formulas for the overlap amplitude of two Bogolyubov quasi-fermion vacuum states that are in some cases more complete than those in the literature are shown. It is pointed out that the name of an "Onishi formula" is assigned in the literature to two different expressions which are related but have different scopes. One of them has what has been described as a sign problem, the other one, due to Onishi and Yoshida, has a more limited scope and no sign problem. I give a short proof of the latter, whose derivation is missing in the paper by Onishi and Yoshida, and a new, combinatoric, proof of an equivalent formula recently derived by Robledo.
