According to professor Wen's string-net theory, electrons can be viewed as the elementary excitations of string-net objects. Just like the phonons and magnons are the elementary excitations of crystals and spin systems, respectively.
But as we know, the "particle number" of phonons and magnons are not conserved since the statistical ensembles of crystal and spin-system are both canonical ensembles, so the"particle number" of phonons and magnons are not well defined. Of course there are no chemical potentials $\mu$ for them.
So I want to know whether the "particle number" of "electrons" is well defined in Wen's string-net theory? And what kind of statistical ensemble does the string-net system belong to,a canonical ensemble or a grand canonical ensemble?
Thank you very much.