Deformed Lorentz Symmetry and High-Energy Astrophysics (III)

TL;DR

This paper explores the theoretical framework of deformed Lorentz symmetry at high energies, its possible extensions to deformed Poincaré symmetry, and connections to models involving extra space-time dimensions, with implications for ultra-high energy cosmic-ray physics.

Contribution

It advances the understanding of how deformed Lorentz symmetry can be extended to deformed Poincaré symmetry and relates these ideas to models with extra space-time dimensions and Finsler algebra extensions.

Findings

Proposes links between deformed relativistic kinematics and space-time dimensions.

Analyzes the limitations of the Kirzhnits-Chechin model.

Suggests extensions of models using Finsler algebras and Magueijo-Smolin transformations.

Abstract

Lorentz symmetry violation (LSV) can be generated at the Planck scale, or at some other fundamental length scale, and naturally preserve Lorentz symmetry as a low-energy limit (deformed Lorentz symmetry, DLS). DLS can have important implications for ultra-high energy cosmic-ray physics (see papers physics/0003080 - hereafter referred to as I -, astro-ph/0011181 and astro-ph/0011182, and references quoted in these papers). A crucial question is how DLS can be extended to a deformed Poincar\'e symmetry (DPS), and what can be the dynamical origin of this phenomenon. In a recent paper (hep-th/0208064, hereafter referred to as II), we started a discussion of proposals to identify DPS with a symmetry incorporating the Planck scale (like doubly special relativity, DSR) and suggested new ways in similar directions. Implications for models of quadratically deformed relativistic kinematics (QDRK) and linearly deformed relativistic kinematics (LDRK) were also discussed. We pursue here our study of these basic problems, focusing on the possibility to relate deformed relativistic kinematics (DRK) to new space-time dimensions and compare our QDRK model, in the form proposed since 1997, which the Kirzhnits-Chechin (KCh) and Sato-Tati (ST) models. It is pointed out that, although the KCh model does not seem to work such as it was formulated, our more recent proposals can be related to suitable extensions of this model generalizing the Finsler algebras (even to situations where a preferred physical inertial frame exists) and using the Magueijo-Smolin transformation as a technical tool.