Topological Invariants and Anyonic Propagators
نویسنده
چکیده
We obtain the Hausdorff dimension, h = 2− 2s, for particles with fractional spins in the interval, 0 ≤ s ≤ 0.5, such that the manifold is characterized by a topological invariant given by, W = h + 2s − 2p. This object is related to fractal properties of the path swept out by fractional spin particles, the spin of these particles, and the genus ( number of anyons ) of the manifold. We prove that the anyonic propagator can be put into a path integral representation which gives us a continuous family of Lagrangians in a convenient gauge. The formulas for, h and W, were obtained taking into account the anyon model as a particle-flux system and by a qualitative inference of the topology. PACS numbers: 11.10.Ef; 03.65.Db
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