Mixing coproducts for theories with particle-dependent relativistic properties

TL;DR

This paper explores how deformed relativistic symmetries, influenced by Planck-scale effects, can vary depending on particle type, introducing mixing coproducts to describe energy-momentum conservation in such scenarios.

Contribution

It introduces the concept of mixing coproducts for particle-dependent deformed relativistic symmetries, expanding the mathematical framework for these theories.

Findings

Mixing coproducts govern energy-momentum conservation in particle-dependent scenarios.

Examples illustrate how relativistic properties can differ among particles.

Relevance to neutrino and composite particle relativistic property proposals.

Abstract

We analyze a few illustrative examples of scenarios in which relativistic symmetries are deformed by Planck-scale effects in particle-type-dependent manner. The novel mathematical structures required by such scenarios are the mixing coproducts, which govern the (deformed) law of conservation of energy and momentum when particles with different relativistic properties interact. We also comment on the relevance of these findings for recent proposals concerning the possibility that neutrinos might have relativistic properties which are different from those of photons and/or the possibility that composite particles might have relativistic properties which are different from those of fundamental ones.