  A general action for particles faster than light is presented. It is
demonstrated that this action is invariant under reparametrizations. For
several cases, it is shown that in the high velocity regime the action is
invariant under anisotropic space-time transformation and at quantum level the
system has fractal behavior. For those cases, it is shown that the action
describes a particle in Finsler geometry and equivalent to one dimensional
field theory in a curved space, where the metric depends on temporal
derivatives.
