**(1)** As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" Hilbert space $V$ would be $V=W_0\oplus W_1\oplus W_2\oplus W_3\oplus...$ , and further we can define creation and annihilation operators which satisfy commutation(anticommutation) relations for bonsons(fermions).

So my first question is, do we also have a "second quantization theory" for anyons like bosons and fermions?

**(2)** Generally speaking, anyons can only happen in 2D. Is this conclusion based on the assumption that the particles are **point-like**?

In Kitaev's toric code model, the quasiparticles are **point-like** due to the **local operators** in the Hamiltonian. My question is, in 3D case, whether there exists a simple model whose Hamiltonian contains **local operators** and **spatially extended operators**, so that it has both poit-like quasiparticles(say, $\mathbf{e}$) and knot-like quasiparticles(say, $\mathbf{m}$), then the $\mathbf{e}$ and $\mathbf{m}$ particles have nontrivial mutual statistics in 3D?

This post imported from StackExchange Physics at 2014-03-09 08:46 (UCT), posted by SE-user K-boy