伪超对称量子力学：一般情况，正交超对称，约化和玻色化
Pseudosupersymmetric quantum mechanics: General case, orthosupersymmetries, reducibility, and bosonization
摘要：
在描述带电矢量介子与恒定磁场相互作用的新Kemmer方程的背景下，引入了基于赝费米子的赝超对称量子力学（PsSSQM）.在这里，我们构造了完全明确的解决方案，其实现方面的两个超势，无论是平等或不平等的。我们证明了任何正交超对称量子力学系统都具有伪超对称性，并给出了伪超对称系统可用二阶正交超对称描述的条件。我们提出了两个新的矩阵实现的PsSSQM的广义变形振子代数（GDOA）的生成元，并将它们的情况下，相等或不相等的超势，分别。我们证明，这些矩阵实现是完全可约的，其不可约的组件提供了两个不同的玻色化运营商实现PsSSQM和相应的非线性光谱。我们将这样的结果与以前的一些获得的GDOA连接的$C_3$ -扩展振子代数（其中$C_3 = {\rm Z}_3$）的情况下的线性谱。
英文摘要：
Pseudosupersymmetric quantum mechanics (PsSSQM), based upon the use of pseudofermions, was introduced in the context of a new Kemmer equation describing charged vector mesons interacting with an external constant magnetic field. Here we construct the complete explicit solution for its realization in terms of two superpotentials, both equal or unequal. We prove that any orthosupersymmetric quantum mechanical system has a pseudosupersymmetry and give conditions under which a pseudosupersymmetric one may be described by orthosupersymmetries of order two. We propose two new matrix realizations of PsSSQM in terms of the generators of a generalized deformed oscillator algebra (GDOA) and relate them to the cases of equal or unequal superpotentials, respectively. We demonstrate that these matrix realizations are fully reducible and that their irreducible components provide two distinct sets of bosonized operators realizing PsSSQM and corresponding to nonlinear spectra. We relate such results to some previous ones obtained for a GDOA connected with a $C_3$-extended oscillator algebra (where $C_3 = {\rm Z}_3$) in the case of linear spectra.
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