Topological Invariants and Anyonic Propagators

Details Topological Invariants and Anyonic Propagators Topological Invariants and Anyonic Propagators

1998-03-05

arxiv.org/abs/hep-th/9803043v1

Mod.Phys.Lett. A14 (1999) 1933-1936

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, latex

Scientific paper

10.1142/S0217732399002005

We obtain the Hausdorff dimension, $h=2-2s$, for particles with fractional spins in the interval, $0\leq s \leq 0.5$, such that the manifold is characterized by a topological invariant given by, ${\cal W}=h+2s-2p$. 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 ${\cal W}$, were obtained taking into account the anyon model as a particle-flux system and by a qualitative inference of the topology.

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