Anyon Type
Worldlines
Anyons (2D only):
In 2D, exchange statistics can be any phase e^{iθ}: bosons (0), fermions (π), anyons (anything).
Statistical phase:
ψ → e^{iθ} ψ under exchange. Braiding = double exchange → e^{2iθ}.
Fusion:
e × m → ε in toric code. Fusion rules: a × b = Σ N^c_{ab} c
FQH:
ν=1/3 → e/3 charge, θ=π/3. Laughlin quasiparticle braiding: Aharonov-Bohm phase.
In 2D, exchange statistics can be any phase e^{iθ}: bosons (0), fermions (π), anyons (anything).
Statistical phase:
ψ → e^{iθ} ψ under exchange. Braiding = double exchange → e^{2iθ}.
Fusion:
e × m → ε in toric code. Fusion rules: a × b = Σ N^c_{ab} c
FQH:
ν=1/3 → e/3 charge, θ=π/3. Laughlin quasiparticle braiding: Aharonov-Bohm phase.