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Principle action for particles faster than light

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.