Local Fractional Supersymmetry for Alternative Statistics
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A group theory justification of one dimensional fractional supersymmetry is proposed using an analogue of a coset space, just like the one introduced in $1D$ supersymmetry. This theory is then gauged to obtain a local fractional supersymmetry {\it i.e.} a fractional supergravity which is then quantized {\it à la Dirac} to obtain an equation of motion for a particle which is in a representation of the braid group and should describe alternative statistics. A formulation invariant under general reparametrization is given, by means of a curved fractional superline.
15 pages, latex, no figure
15 pages, latex, no figure