Abstract
A novel approach to study the properties of models with quantum-deformed relativistic symmetries relies on a noncommutative space of worldlines rather than the usual noncommutative spacetime. In this setting, spacetime can be reconstructed as the set of events, that are identified as the crossing of different worldlines. We lay down the basis for this construction for the κ-Poincaré model, analyzing the fuzzy properties of κ-deformed time-like worldlines and the resulting fuzziness of the reconstructed events.
Highlights
Our work lies in the same general framework as relative locality, since our setup is given by deformed relativistic symmetries
These are used to work out the properties of the momentum space, which turns out to be curved, with the Planck scale setting the scale of curvature [26,27,28,29,30]
The space of worldlines can be obtained as the homogeneous space of the Poincaré transformations modulo rotations and time translations, that are the transformations leaving invariant the origin of this space
Summary
We start by reviewing the classical description of worldlines in special relativity, which allows us to establish a correspondence between Minkowski spacetime coordinates xμ and the parameters which identify a worldline, namely its velocity v and intercept at time zero, B. By means of this parameterization we can identify the coordinate velocity vi dxi dx0. Each worldline represents a free massive particle that passes through the spacetime point (0, B) with spatial velocity v This interpretation allows us to describe an especially simple worldline, which we call w0, corresponding to a particle staying at the origin with zero velocity.
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