Deformed Boost Transformations That Saturate at the Planck Scale

TL;DR

This paper derives finite boost transformations within a deformed relativistic framework based on the $kappa$-Poincare algebra, showing they saturate at the Planck scale, supporting a new observer-independent scale in relativity.

Contribution

It introduces a specific form of deformed boost transformations that incorporate the Planck length as an invariant scale, extending the $kappa$-Poincare algebra to finite transformations.

Findings

Deformed boosts saturate at the inverse of the Planck length.

The deformation introduces an observer-independent scale in relativistic transformations.

The transformations are based on the Lorentz sector of the $kappa$-Poincare Hopf algebra.

Abstract

We derive finite boost transformations based on the Lorentz sector of the bicross-product-basis $\kappa$-Poincare' Hopf albegra. We emphasize the role of these boost transformations in a recently-proposed new relativistic theory. We find that when the (dimensionful) deformation parameter is identified with the Planck length, which together with the speed-of-light constant has the status of observer-independent scale in the new relativistic theory, the deformed boosts saturate at the value of momentum that corresponds to the inverse of the Planck length.