Spacetime and Deformations of Special Relativistic Kinematics

José Manuel Carmona,José Luis Cortés,José Javier Relancio

doi:10.3390/sym11111401

José Manuel Carmona, José Luis Cortés + Show 1 more

Open Access

https://doi.org/10.3390/sym11111401

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Journal: Symmetry	Publication Date: Nov 12, 2019
Citations: 13	License type: CC BY 4.0

Affiliation: Universidad de Zaragoza

Abstract

A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a model including single- or multi-interaction processes, for which absolute locality in terms of canonical spacetime coordinates is lost. We discuss the different alternatives for observable effects in the propagation of a particle over very large distances that emerge from the new notion of spacetime. A central ingredient in the discussion is the cluster decomposition principle, which can be used to favor some alternatives over the others.

Highlights

IntroductionWe start from the classical notion of spacetime based on the theory of Special Relativity (SR)
We start from the classical notion of spacetime based on the theory of Special Relativity (SR).The invariance of the equations of motion for different inertial reference frames related by Lorentz transformations led Einstein to go from the notion of absolute time and space to the notion of spacetime in SR
When the deformation of SR kinematics does not involve a modification of the expression of the momentum of the in and out states in terms of the momenta of the particles, one can still have an implementation of the deformation in a local quantum theory framework [28]

Summary

Introduction

We start from the classical notion of spacetime based on the theory of Special Relativity (SR). The other path to explore the modification of the notion of spacetime is to implement at the classical level a deformation of the SR kinematics (modification of the energy-momentum relation and/or modification of the total energy-momentum of a system of free particles in terms of the energy-momentum of each particle) in a model for the interaction of particles and try to see which is the associated notion of spacetime in this framework. This is the path that we follow in this work identifying the main obstacles and the different alternatives to overcome them. A particular objective of this study is to try to answer the question of whether there will be observable effects of deformation of the notion of spacetime when considering the propagation of particles over very large distances

Deformation of SR Kinematics

Single-Interaction Process

Multi-Interaction Process

Observable Effects in the Propagation of a Particle over Very Large Distances

Conclusions and Outlook