Principle action for particles faster than light

TL;DR

This paper introduces a new action principle for faster-than-light particles, demonstrating invariance properties and fractal quantum behavior, linking the system to Finsler geometry and curved space field theories.

Contribution

It presents a novel reparametrization-invariant action for superluminal particles, connecting it to Finsler geometry and anisotropic space-time transformations.

Findings

Action is invariant under reparametrizations.

High velocity regime exhibits anisotropic space-time invariance.

Quantum behavior shows fractal characteristics.

Abstract

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.