Deformed Special Relativity in Position Space

TL;DR

This paper explores extending deformed special relativity from momentum space to position space, ensuring invariance of key ratios and analyzing implications for transformations, mass gain, and Lorentz transformations.

Contribution

It introduces a consistent framework for deformed special relativity in position space, linking energy-dependent constants to active and passive Lorentz transformations.

Findings

Active transformations deviate from standard at high velocities

Relativistic mass gain is affected by deformations

Passive Lorentz-transformations are constructed and analyzed

Abstract

We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a parametrization in terms of an energy dependent speed of light, and an energy dependent Planck's constant, we are able to formulate simple requirements that completely determine the active transformations in position space. These deviate from the standard transformations for large velocities of the observed object. Some examples are discussed, and it is shown how the relativistic mass gain of a massive particle is affected. We finally study the construction of passive Lorentz-transformations.