Planck-scale modified dispersion relations and Finsler geometry

Near Scale Invariance with Modified Dispersion Relations

Planck-Scale Phenomenology and Symmetry in Randers–Finsler Spaces

Lorentz Violation is a common feature of Planck-scale phenomenology. We show that the symmetry of Randers spaces deduces a modified dispersion relation, which takes the quantum gravity effects into account. The counterparts of the Lorentz transformation in the Einstein’s Special Relativity are presented explicitly. The coordinate transformations are unitary and form a group. Generators and alge...

Quantum Geometry and the Planck Scale

In this contribution I would like to discuss some of the conceptual and physical issues surrounding the approach to noncommutative geometry coming out of quantum groups and braided groups, in somewhat greater depth than I had time for in my lecture in Goslar. The discussion is intended to be intelligible to non-specialists and may hopefully serve as an invitation to the field. Technical materia...

Modified Dispersion Relations and trans-Planckian Physics

We consider modified dispersion relations in quantum field theory on curved space-time. Such relations, despite breaking the local Lorentz invariance at high energy, are considered in several phenomenological approaches to quantum gravity. Their existence involves a modification of the formalism of quantum field theory, starting from the problem of finding the scalar Green’s functions up to the...

Modified dispersion relations and black hole physics

A modified formulation of energy-momentum relation is proposed in the context of doubly special relativity. We investigate its impact on black hole physics. It turns out that such modification will give corrections to both the temperature and the entropy of black holes. In particular this modified dispersion relation also changes the picture of Hawking radiation greatly when the size of black h...