Wick's theorem for other statistics

[MelvinSmith]

Hi all!
I've got a question concerning Wick's theorem. I followed the proof in the book by Fetter and Walecka and it works well for particles with "normal" statistic, that means for bosons and fermons (commuting or anticommuting). But what about anyons, particles which don't commute just with a delta or 1 but with an arbitrary phase factor? I think the proof doesn't apply to such particles. So the question is, if there is a Wick's theorem or something similar for anyons.
Thank you for any help!
Melvin

 

[azntoon]

</code>Yes, there is a Wick's theorem for anyons. The basic idea is the same as for bosons and fermions, but the algebra is more complicated since you have to take into account the phase factor associated with the anyon. In essence, Wick's theorem for anyons states that the expectation value of any product of fields can be expressed as a sum of products of pairwise contractions. However, the form of these contractions is much more complicated than for bosons and fermions, as they involve the phase factor associated with the anyon. A full derivation of Wick's theorem for anyons can be found in the book "Anyons: Quantum Mechanics of Particles with Fractional Statistics" by M. Stone (World Scientific, 1992).