Curved momentum space, locality, and generalized space-time

TL;DR

This paper explores the relationship between curved momentum space and the loss of absolute locality in spacetime, proposing a generalized spacetime to restore locality, with a focus on $or Poincare9$ kinematics.

Contribution

It establishes a clear correspondence between geometric momentum space properties and locality loss, providing a unified framework for $or Poincare9$ kinematics.

Findings

Explicit correspondence between momentum space geometry and locality loss.

Comparison with Hopf algebra framework.

Restoration of locality via generalized spacetime.

Abstract

We establish the correspondence between two apparently unrelated but in fact complementary approaches of a relativistic deformed kinematics: the geometric properties of momentum space and the loss of absolute locality in canonical spacetime, which can be restored with the introduction of a generalized spacetime. This correspondence is made explicit for the case of $\kappa$-Poincar\'e kinematics and compared with its properties in the Hopf algebra framework.