The Pauli exclusion principle and beyond

TL;DR

This paper explores the limitations of the Pauli exclusion principle, discussing how replacing it with wave function skew symmetry introduces new constraints on electron density matrices and affects physical properties like magnetic moments.

Contribution

It analyzes the additional constraints on electron density matrices arising from wave function symmetry, extending the understanding of quantum restrictions beyond the traditional Pauli principle.

Findings

New constraints on electron density matrices are identified.

Implications for spin magnetic moments in multi-electron systems are discussed.

The relationship between the exclusion principle and wave function symmetry is clarified.

Abstract

The Pauli exclusion principle can be stated as inequality $<\psi|\rho|\psi>\le 1$ for the electron density matrix $\rho$. Nowadays it is replaced by skew symmetry of the multi-electron wave function. The replacement leads to numerous additional constraints on $\rho$, which are discussed in this letter together with their physical implications, in particular for spin magnetic moment of a multi-electron system.