[论文解读] Pauli Exclusion Principle and its theoretical foundation

Ilya G. Kaplan|arXiv (Cornell University)|Jan 29, 2019

Quantum and Classical Electrodynamics参考文献 15被引用 6

一句话总结

本文重新审视了泡利不相容原理（PEP）的理论基础，认为仅允许对称和反对称置换态（对应玻色子和费米子）并非一个公设，而是更深层次物理原理的推论。它证明，任意的置换对称性将与粒子的本体性和独立性产生矛盾，意味着自然界中不可能存在非费米子或非玻色子的粒子。

ABSTRACT

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.

研究动机与目标

• 重新评估泡利不相容原理的理论依据，超越其标准公设地位。
• 挑战广泛接受的教科书证明，即仅允许一维置换表示（对称和反对称）。
• 探究简并置换态（高维表示）是否能在物理上实现。
• 考察粒子本体性和独立性对多体波函数结构的影响。
• 得出结论：不相容原理并非公设，而是物理一致性的必然结果，从而排除了非费米子或非玻色子粒子的存在。

提出的方法

• 分析非相对论量子力学中多体波函数的置换对称性。
• 指出标准教科书推导中存在缺陷，这些推导声称仅对称和反对称态是允许的。
• 应用群表示理论对波函数可能的置换对称性进行分类。
• 证明简并置换态会与粒子本体性的基本概念产生矛盾。
• 利用粒子独立性的要求，排除非一维表示作为物理上可行的选项。
• 得出结论：仅对称态（玻色子）和反对称态（费米子）与基本物理原理一致。

实验结果

研究问题

• RQ1 为何自然界中仅出现对称和反对称置换态，这种限制是否具有任意性？
• RQ2 简并置换态（高维表示）是否能在量子系统中实现？
• RQ3 在多体量子系统中违反粒子本体性假设会产生何种物理后果？
• RQ4 自旋统计连接（SSC）是基本定律，还是更深层原理的推论？
• RQ5 未来发现是否可能揭示既非费米子也非玻色子的基本粒子？

主要发现

• 教科书中声称仅允许对称和反对称态的证明是错误的，其推理存在缺陷。
• 简并置换态会与粒子本体性和独立性的基本概念产生矛盾。
• 仅允许一维置换表示（对称和反对称）并非公设，而是物理一致性的必然结果。
• 仅存在费米子和玻色子并非偶然，而是源于一致量子描述的要求。
• 由于其波函数对称性与粒子本体性不相容，自然界中不可能实现非费米子或非玻色子粒子。
• 泡利不相容原理在理论上得到了物理原理的充分支持，而非任意公设。