Abstract
A new proposal for the notion of spacetime in a relativistic generalization of special relativity based on a modification of the composition law of momenta is presented. Locality of interactions is the principle which defines the spacetime structure for a system of particles. The formulation based on $\kappa$-Poincar\'e Hopf algebra is shown to be contained in this framework as a particular example.
Highlights
There is a consensus that the classical spacetime structure of special relativity (SR) will probably have to be modified in a quantum theory of gravity
Κ-Minkowski, was inspired by the Hopf algebra known as κ-Poincare [11,12], in which a modified composition law (MCL) for the momenta, a modified Casimir and an implementation of nonlinear boosts in momentum space are chosen in order to satisfy the relativity principle
In this work we explore the possibility to look for a new spacetime, whose coordinates differ from the spacetime coordinates canonically conjugated to the momentum variables, such that absolute locality is compatible with the modified composition law
Summary
There is a consensus that the classical spacetime structure of special relativity (SR) will probably have to be modified in a quantum theory of gravity (see, for example, the different contributions in Ref. [1]). A number of works have explored the connection, through the product of plane waves, between a deformation of the Heisenberg algebra (phase-space commutation relations) and energy-momentum modified composition laws In this context, the spacetime proposed by Snyder has got a MCL associated to it, as shown in Ref. [10]; in this case, and due to the fact that this is a covariant model, there is no modification in the dispersion relation nor in the Lorentz transformations Another noncommutative spacetime model, κ-Minkowski, was inspired by the Hopf algebra known as κ-Poincare [11,12], in which a MCL for the momenta, a modified Casimir (the MDR) and an implementation of nonlinear boosts in momentum space are chosen in order to satisfy the relativity principle. We will see that the relation between the κ-Poincare Hopf algebra and κ-Minkowski spacetime through the pairing procedure is of this type, but the idea of locality in the new spacetime gives rise to other possible extensions of the phase space of SR
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