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.

v1: 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

References in corpus (4)

• Noncommutative Black Hole Thermodynamics
• Charged rotating noncommutative black holes
• Hausdorff dimension of a particle path in a quantum manifold
• Minimal Scales from an Extended Hilbert Space

Cited by in corpus (15)

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• Modified Newton's Law of Gravitation Due to Minimal Length in Quantum Gravity
• Neutrino Decoherence from Generalised Uncertainty
• Exotic fermionic fields and minimal length
• The Influence of Approximation in Generalized Uncertainty Principle on Black Hole Evaporation
• Reconciling microscopic and macroscopic tests of the Compton-Schwarzschild correspondence
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Effect of the Minimal Length on Bose-Einstein Condensation in the Relativistic Ideal Bose Gas
• Lorentz Force and Ponderomotive Force in the Presence of a Minimal Length
• Quantum Hairy Black Hole Formation and Horizon Quantum Mechanics
• Relativistic generalised uncertainty and the corrected vacuum energy
• Effective models of non-singular quantum black holes