Dyson's three-fold way

Dyson's three-fold way classifies particles based on how their intrinsic spin behaves under symmetry transformations. It divides particles into three types: 1. **Bosons** (integer spin): Their wavefunctions are symmetric when two particles are exchanged. They can occupy the same quantum state, like photons. 2. **Fermions** (half-integer spin): Their wavefunctions are antisymmetric upon exchange, obeying the Pauli exclusion principle, like electrons. 3. **Anyons** (neither bosons nor fermions): Occur in two-dimensional systems, with properties interpolating between bosons and fermions, featuring unique statistical behaviors. This framework helps understand the fundamental nature of particles.