The modern state of the Pauli Exclusion Principle (PEP) is discussed. PEP can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is the so-called spin-statistics connection (SSC). As we will discuss, the physical reasons why SSC exists are still unknown. On the other hand, according to PEP, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, both belong to one-dimensional representations of the permutation group, all other types of permutation symmetry are forbidden; whereas the solution of the Schrodinger equation may have any permutation symmetry. It is demonstrated that the proof in some textbooks on quantum mechanics that only symmetric and antisymmetric states can exist is wrong. However, the scenarios, in which arbitrary permutation symmetry (degenerate permutation states) is permitted, lead to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature of particles only in nondegenerate permutation states (symmetric and antisymmetric) is not accidental and so-called symmetrization postulate should not be considered as a postulate, since all other symmetry options for the total wave function may not be realized. From this an important conclusion follows: we may not expect that in the future some unknown elementary particles can be discovered that are not fermions or bosons.

中文翻译：

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泡利不相容原理及其理论证明问题1

讨论了泡利排除原则 (PEP) 的现代状态。PEP 可以从两个角度考虑。一方面，它断言具有半整数自旋（费米子）的粒子由反对称波函数描述，而具有整数自旋（玻色子）的粒子由对称波函数描述。这就是所谓的自旋统计连接 (SSC)。正如我们将要讨论的，SSC 存在的物理原因仍然未知。另一方面，根据PEP，总波函数的置换对称性只能有两种类型：对称或反对称，都属于置换群的一维表示，禁止所有其他类型的置换对称性；而薛定谔方程的解可以具有任何置换对称性。事实证明，一些量子力学教科书中关于只有对称和反对称状态才能存在的证明是错误的。然而，允许任意置换对称（退化置换状态）的场景会导致与粒子同一性及其独立性的概念相矛盾。因此，仅在非简并置换状态（对称和反对称）中存在粒子的性质并非偶然，不应将所谓的对称化假设视为假设，因为可能无法实现总波函数的所有其他对称选项. 由此得出一个重要结论：我们可能不会期望将来会发现一些不是费米子或玻色子的未知基本粒子。