1301.7609 (Ivan Arraut)

Relative locality and relative Co-locality as extensions of the
Generalized Uncertainty Principle    [PDF]

Ivan Arraut

We interpret Relative locality as the variation of the Ultraviolet (UV) cut-off with respect to the observer's position relative to an event in agreement with an extended version of the Generalized Uncertainty Principle (GUP). As a consequence there is a natural red-shift effect for the events when they are observed at a given distance x. We then introduce the concept of Relative Co-locality as the variation of the infrared (IR) cut-off with respect to the observer's momentum relative to the event. As a consequence, there is a natural blue-shift effect for the events when the observer has a given momentum p with respect to them. Both effects are dual each other inside the formalism of quantum groups $SU(n)_q$ symmetric Heisenberg algebras and their q-Bargmann Fock representations. When Relative locality and Co-locality are introduced, the q-deformation parameter takes the form $q\approx 1+\sqrt{\frac{\vert p\vert \vert x\vert}{r_\Lambda m_{pl}c}}$ with the Relative Co-locality defined as $\Delta P\approx \frac{\vert p\vert}{r_\Lambda}\Delta X$, where $r_\Lambda=\frac{1}{\sqrt{\Lambda}}$ is the scale defined by the Cosmological Constant $\Lambda$, $\Delta X$ is a scale of position or time associated with the event, p and x are the momentum and position of the observer relative to the event.

View original: http://arxiv.org/abs/1301.7609