Modified Relativity from the kappa-deformed Poincare Algebra

TL;DR

This paper explores modifications to special relativity derived from the $$-deformed Poincare algebra, analyzing phenomena like Doppler effect and Michelson-Morley experiment with implications for quantum mechanics and field theory.

Contribution

It develops series expansions of generalized Lorentz transformations based on the $$-deformed Poincare algebra, highlighting assumptions and limits of the deformation parameter.

Findings

Lower bounds on deformation parameter: 90 eV from Doppler effect

Lower bounds on deformation parameter: 250 keV from Michelson-Morley experiment

Discussed corrections to Casimir effect and Thomas precession

Abstract

The theory of the $\kappa$-deformed Poincare algebra is applied to the analysis of various phenomena in special relativity, quantum mechanics and field theory. The method relies on the development of series expansions in $\kappa^{-1}$ of the generalised Lorentz transformations, about the special-relativistic limit. Emphasis is placed on the underlying assumptions needed in each part of the discussion, and on in principle limits for the deformation parameter, rather than on rigorous numerical bounds. In the case of the relativistic Doppler effect, and the Michelson-Morley experiment, comparisons with recent experiemntal tests yield the relatively weak lower bounds on $\kappa c$ of 90eV and 250 keV, respectively. Corrections to the Casimir effect and the Thomas precession are also discussed.