The Pauli exclusion principle and beyond

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.