# Quantum speed limit for a relativistic electron in the noncommutative phase space

## TL;DR

This paper investigates how noncommutativity in phase space affects the speed of a relativistic electron, revealing that it can surpass the speed of light, thus indicating a violation of Lorentz invariance.

## Contribution

It demonstrates that noncommutativity can lead to superluminal speeds in relativistic quantum systems, challenging traditional notions of Lorentz invariance.

## Key findings

- Electron wave packet can travel faster than light due to noncommutativity.
- Noncommutativity causes violation of Lorentz invariance in relativistic quantum mechanics.
- The study links noncommutative geometry with fundamental speed limits.

## Abstract

The influence of the noncommutativity on the average speed of a relativistic electron interacting with a uniform magnetic field within the minimum evolution time is investigated. We find that it is possible for the wave packet of the electron to travel faster than the speed of light in vacuum because of the noncommutativity. It suggests that due to the noncommutativity, Lorentz invariance is violated in the relativistic quantum mechanics region.