Physics on Smallest Scales - An Introduction to Minimal Length Phenomenology

TL;DR

This paper reviews the concept of a minimal length in quantum gravity, exploring its formalism and phenomenological implications through effective models, aimed at graduate students and non-specialists.

Contribution

It provides a comprehensive overview of minimal length phenomenology using effective models like the generalized uncertainty principle and non-commutative geometry.

Findings

Effective models can make model-independent experimental predictions

Pedagogical examples illustrate minimal length effects

Focus on phenomenological implications of quantum gravity theories

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.