Fermion

A fermion is a particle with half-integer Spin (12\frac{1}{2}, 32\frac{3}{2}, ...). The wavefunction of a system of NN fermions changes sign when subject to a coordinate permutation:

Pijψ(r1,…,ri,…,rj,…,rN)=−ψ(r1,…,rj,…,ri,…,rN)P_{ij}\psi(\mathbf{r}_{1},\ldots,\mathbf{r}_{i},\ldots,\mathbf{r}_{j},\ldots,\mathbf{r}_{N})=-\psi(\mathbf{r}_{1},\ldots,\mathbf{r}_{j},\ldots,\mathbf{r}_{i},\ldots,\mathbf{r}_{N})

PijP_{ij} is the permutation operator. This wavefunction is said to be antisymmetric (or odd) under particle exchange. Their behavior in matter is described by the Fermi-Dirac distribution.

Fermions are subject to the Pauli exclusion principle.

Origin

The existence of fermions as a separate category arises from the indistinguishability of particles caused by the uncertainty principle.