A note on DSR-like approach to space-time

Abstract

In this note we discuss the possibility to define a space-time with a DSR based approach. We show that the strategy of defining a non linear realization of the Lorentz symmetry with a consistent vector composition law cannot be reconciled with the extra request of an invariant length (time) scale. The latter request forces to abandon the group structure of the translations and leaves a space-time structure where points with relative distances smaller or equal to the invariant scale can not be unambiguously defined.

5 pages, 1 figure

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Cited by in corpus (9)

• Taming nonlocality in theories with Planck-scale-deformed Lorentz symmetry
• Modifications to Lorentz invariant dispersion in relatively boosted frames
• Relative-locality distant observers and the phenomenology of momentum-space geometry
• Deformed Special Relativity as an effective theory of measurements on quantum gravitational backgrounds
• Inertial frames without the relativity principle
• Modified Special Relativity on a fluctuating spacetime
• From Noncommutative Sphere to Nonrelativistic Spin
• $\kappa$-Poincaré phase space: speed of massless particles and relativity of spacetime locality
• Relativity principle with a low energy invariant scale