Boson

A boson is a particle with integer Spin (0,1, ...). The wavefunction of a system of NN bosons does not change 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 symmetric (or even) under particle exchange. Their behavior in matter is described by the Bose-Einstein distribution.

Origin

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