Self-consistency in Theories with a Minimal Length

The aim of this paper is to clarify the relation between three different approaches of theories with a minimal length scale: A modification of the Lorentz-group in the 'Deformed Special Relativity', theories with a 'Generalized Uncertainty Principle' and those with 'Modified Dispersion Relations'. It is shown that the first two are equivalent, how they can be translated into each other, and how the third can be obtained from them. An adequate theory with a minimal length scale requires all three features to be present.Comment: typos corrected, published with new title following referee's advic

TeV Mini Black Hole Decay at Future Colliders

It is generally believed that mini black holes decay by emitting elementary particles with a black body energy spectrum. The original calculation lead to the conclusion that about the 90% of the black hole mass is radiated away in the form of photons, neutrinos and light leptons, mainly electrons and muons. With the advent of String Theory, such a scenario must be updated by including new effects coming from the stringy nature of particles and interactions.By taking for granted that black holes can be produced in hadronic collisions, then their decay must take into account that: (i) we live in a D3-Brane embedded into an higher dimensional bulk spacetime; (ii) fundamental interactions, including gravity, are unified at TeV energy scale. Thus, the formal description of the Hawking radiation mechanism has to be extended to the case of more than four spacetime dimensions and include the presence of D-branes. Furthermore, unification of fundamental interactions at an energy scale many order of magnitude lower than the Planck energy implies that any kind of fundamental particle, not only leptons, is expected to be emitted. A detailed understanding of the new scenario is instrumental for optimal tuning of detectors at future colliders, where, hopefully, this exciting new physics will be tested. In this article we review higher dimensional black hole decay, considering not only the emission of particles according to Hawking mechanism, but also their near horizon QED/QCD interactions. The ultimate motivation is to build up a phenomenologically reliable scenario, allowing a clear experimental signature of the event.Comment: 22 pages, 9 figures, 4 tables; ``quick review'' for Class. and Quantum Gra

Minimal Length Scale Scenarios for Quantum Gravity

We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize what can be learned from different approaches to a theory of quantum gravity. Then we discuss some models that have been developed to implement a minimal length scale in quantum mechanics and quantum field theory. These models have entered the literature as the generalized uncertainty principle or the modified dispersion relation, and have allowed the study of the effects of a minimal length scale in quantum mechanics, quantum electrodynamics, thermodynamics, black-hole physics and cosmology. Finally, we touch upon the question of ways to circumvent the manifestation of a minimal length scale in short-distance physics.Comment: Published version available at http://www.livingreviews.org/lrr-2013-