Mixing coproducts for theories with particle-dependent relativistic properties

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.

References in corpus (21)

• Lorentz-Violating Extension of the Standard Model
• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• Testable scenario for Relativity with minimum-length
• Quantum Spacetime Phenomenology
• Generalized Lorentz invariance with an invariant energy scale
• Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510
• Cosmic Ray and Neutrino Tests of Special Relativity
• Doubly Special Relativity
• The principle of relative locality
• Prospects for constraining quantum gravity dispersion with near term observations
• GRBs Neutrinos as a Tool to Explore Quantum Gravity induced Lorentz Violation
• Neutrino Interferometry for High-Precision Tests of Lorentz Symmetry with IceCube
• Hopf-algebra description of noncommutative-spacetime symmetries
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Relative locality and the soccer ball problem
• IceCube and GRB neutrinos propagating in quantum spacetime
• On the fate of Lorentz symmetry in relative-locality momentum spaces
• Upper Limits from HESS AGN Observations in 2005-2007
• The classical basis for $\kappa$-deformed Poincaré (super)algebra and the second $\kappa$-deformed supersymmetric Casimir
• Quantum-gravity-induced dual lensing and IceCube neutrinos
• Snyder Momentum Space in Relative Locality

Cited by in corpus (4)

• Equivalence Principle in Classical and Quantum Gravity
• The Equivalence Principle as a Noether Symmetry
• Neutrinos as possible probes for quantum gravity
• Testing the universality of quantum gravity theories with cosmic messengers in the context of DSR theories