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A general action for particles faster than light is presented. It isdemonstrated that this action is invariant under reparametrizations. Forseveral cases, it is shown that in the high velocity regime the action isinvariant under anisotropic space-time transformation and at quantum level thesystem has fractal behavior. For those cases, it is shown that the actiondescribes a particle in Finsler geometry and equivalent to one dimensionalfield theory in a curved space, where the metric depends on temporalderivatives.

Principle action for particles faster than light