September 16, 2015

Speaker: Professor I. G. Kaplan (Materials Research Institute, UNAM, Mexico)
Title: Discovery and the modern state of the Pauli Exclusion Principle. Can it be proved?
Abstract: In the introduction, we will present how Wolfgang Pauli came to the formulation of his exclusion principle, and the dramatic history of the discovery of the fundamental quantum-mechanical conception of spin. Then we will discuss the modern state of the Pauli Exclusion Principle (PEP). If all experimental data agree with the PEP and the best to day limit on the violation of the PEP is negligible¹, its theoretical foundations are still absent.
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 a so-called spin-statistics connection. As we will discuss, the reasons the spin-statistics connection exists are still unknown. On the other hand, according to the PEP, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric; all other types of permutation symmetry are forbidden. However, the solutions of the Schrödinger equation may belong to any representation of the permutation group, including the multi-dimensional ones. It is demonstrated that the proofs of the PEP in some textbooks on quantum mechanics, including the famous course of Landau and Lifshitz, are incorrect. The indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of PEP.
The heuristic arguments have been given in favor that the existence in nature only one-dimensional permutation representations (symmetric and antisymmetric) is not accidental. As follows from the analysis of possible scenarios, the permission of multi-dimensional representations of the permutation group leads to contradictions with the concept of particle identity and their independence². Thus, the prohibition of the degenerate permutation stated by the PEP follows from the general physical assumptions underlying quantum theory.