Physics on Smallest Scales - An Introduction to Minimal Length Phenomenology

Abstract

Many modern theories which try to unify gravity with the Standard Model of particle physics, as e.g. string theory, propose two key modifications to the commonly known physical theories: i) the existence of additional space dimensions; ii) the existence of a minimal length distance or maximal resolution. While extra dimensions have received a wide coverage in publications over the last ten years (especially due to the prediction of micro black hole production at the LHC), the phenomenology of models with a minimal length is still less investigated. In a summer study project for bachelor students in 2010 we have explored some phenomenological implications of the potential existence of a minimal length. In this paper we review the idea and formalism of a quantum gravity induced minimal length in the generalised uncertainty principle framework as well as in the coherent state approach to non-commutative geometry. These approaches are effective models which can make model-independent predictions for experiments and are ideally suited for phenomenological studies. Pedagogical examples are provided to grasp the effects of a quantum gravity induced minimal length. This article is intended for graduate students and non-specialists interested in quantum gravity.

arXiv commentv1: 10 pages, 3 figures, paper originated by a summer study for bachelor students at the University of Frankfurt; v2: 11 pages, 3 figures, minor modifications, version accepted for publication on European Journal of Physics

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• Quantum Hairy Black Hole Formation and Horizon Quantum Mechanics
• Hartmann potential with a minimal length and generalized recurrence relations for matrix elements
• Emergent GUP from Modified Hawking Radiation in Einstein-NED Theory
• Relativistic generalised uncertainty and the corrected vacuum energy
• Effective models of non-singular quantum black holes