arXiv 1902.004992019-02quant-phmath-phmath.MP

泡利不相容原理及其理论基础

Pauli Exclusion Principle and its theoretical foundation

I. G. Kaplan

备注：: 24 pages, 2 figures, The Pauli exclusion principle is theoretically subtantiated. From the presented proof it follows that we may not expect that in future some unknown elementary particles that are not fermions or bosons can be discovered

摘要：

讨论了泡利不相容原理（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的粒子（费米子）由反对称波函数描述，而具有整数自旋的粒子（玻色子）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，全波函数的置换对称性只能有两种类型：对称或反对称，两者都属于置换群的一维表示，所有其他类型的置换对称性都是禁止的;而薛定谔方程的解可以有任何置换对称性。证明了在一些广泛使用的量子力学教科书中关于置换群只能存在对称态和反对称态的证明是错误的。然而，允许任意排列对称（简并排列态）的情况导致与粒子身份及其独立性的概念相矛盾。因此，在我们的自然粒子只存在于非简并置换态（对称和反对称）不是偶然的，所谓的对称化假设可能不被认为是一个假设，因为所有其他的对称选项的总波函数可能无法实现。由此可以得出一个重要的结论：我们可能不会期望在未来发现一些非费米子或玻色子的未知基本粒子。

英文摘要：

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 Schrödinger equation may have any permutation symmetry. It is demonstrated that the proof in some widespread textbooks on quantum mechanics that only symmetric and antisymmetric states (one-dimensional representations of the permutation group) can exist is wrong. However, the scenarios, in which an 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 particles only in nondegenerate permutation states (symmetric and antisymmetric) is not accidental and so-called symmetrization postulate may 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 future some unknown elementary particles can be discovered that are not fermions or bosons.

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英文摘要：

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