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**Physics on the smallest scales: an introduction to minimal length phenomenology.**
*(English)*
Zbl 1271.83034

Summary: Many modern theories which try to unify gravity with the Standard Model of particle physics, such as e.g. string theory, propose two key modifications to the commonly known physical theories: the existence of additional space dimensions; 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 Large Hadron Collider), 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 generalized 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 paper is intended for graduate students and non-specialists interested in quantum gravity.

### MSC:

83C45 | Quantization of the gravitational field |