Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation

Abstract

The Pauli exclusion principle (PEP) can be considered from two aspects. First, it asserts that particles that have half-integer spin (fermions) are described by antisymmetric wave functions, and particles that have integer spin (bosons) are described by symmetric wave functions. It is called spin-statistics connection (SSC). The physical reasons why SSC exists are still unknown. On the other hand, PEP is not reduced to SSC and can be consider from another aspect, according to it, the permutation symmetry of the total wave function can be only of two types: symmetric or antisymmetric. They both belong to one-dimensional representations of the permutation group, while other types of permutation symmetry are forbidden. However, the solution of the Schrödinger equation may have any permutation symmetry. We analyze this second aspect of PEP and demonstrate that proofs of PEP in some wide-spread textbooks on quantum mechanics, basing on the indistinguishability principle, are incorrect. The indistinguishability principle is insensitive to the permutation symmetry of wave function. So, it cannot be used as a criterion for the PEP verification. However, as follows from our analysis of possible scenarios, the permission of states with permutation symmetry more general than symmetric and antisymmetric leads to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature particles only in symmetric and antisymmetric permutation states is not accidental, since all symmetry options for the total wave function, except the antisymmetric and symmetric, cannot be realized. From this an important conclusion follows, we may not expect that in future some unknown elementary particles that are not fermions or bosons can be discovered.

Modern State of the Conventional DFT Method Studies and the Limits Following from the Quantum State of the System and Its Total Spin

“…It was proved for an arbitrary point group, but it is correct for any finite group. For the permutation group, this result was used in my publications [24,59,60] in analysis of the foundations of PEP. In these articles, I analyzed the case when PEP is not fulfilled and except of symmetrical and antisymmetrical states, an arbitrary permutation symmetry, including degenerate permutation states, are permitted.…”

“…The arguments presented in Refs. [24,59,60], see also book [5], can be considered as a theoretical substantiation of PEP. They explained why in our Nature only completely symmetric or antisymmetric states, corresponding to onedimensional representations of the permutation group, are realized.…”

KLD: A Program to Elucidate the Localization of the Fermi and Coulomb Holes in Molecular Systems

“…From the early principles of quantum mechanics, it is known that two main mechanisms govern the electron-electron interaction in atoms, molecules, and solids. The first one arises as a consequence of the classical electrostatic repulsion between electrons [2,3]; whereas the second one has a quantum origin, being associated to the antisymmetric character of Fermion wavefunctions and later formalized in the Pauli exclusion principle [4]. In order to provide context to the present work, it is important to annotate that both interaction mechanisms delineate regions around electrons where the probability to find another electron is negligible.…”

Ab Initio Calculations of Transport and Optical Properties of Dense Zr Plasma Near Melting

“…In such calculations, liquid metal is treated as a strongly coupled degenerate plasma. This means that the electronic subsystem should be described by a wave function that is antisymmetric in the permutation of any two electrons [36]. In DFT this is usually achieved by using a determinant composed of one-electron wave functions.…”