A new Doubly Special Relativity theory from a quantum Weyl-Poincare algebra

TL;DR

This paper introduces a novel Doubly Special Relativity theory derived from a quantum Weyl-Poincare algebra, featuring unique momentum saturation and deformed position operators, expanding the framework of relativistic physics at Planck scale.

Contribution

It proposes a new DSR theory based on a quantum Weyl-Poincare algebra with distinctive momentum and position operator features, differing from previous models.

Findings

Deformed momentum representation and finite boost transformations analyzed.

Range of rapidity, energy, and momentum explicitly studied.

New momentum saturation and deformed position operators identified.

Abstract

A mass-like quantum Weyl-Poincare algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, a new relativistic theory with two observer-independent scales (or DSR theory). Deformed momentum representation, finite boost transformations, range of rapidity, energy and momentum, as well as position and velocity operators are explicitly studied and compared with those of previous DSR theories based on kappa-Poincare algebra. The main novelties of the DSR theory here presented are the new features of momentum saturation and a new type of deformed position operators.