Living Reviews in Relativity

"Minimal Length Scale Scenarios for Quantum Gravity"
Sabine Hossenfelder 

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1 Introduction
2 A Minimal History
3 Motivations
3.1 Thought experiments
3.2 String theory
3.3 Loop Quantum Gravity and Loop Quantum Cosmology
3.4 Quantized conformal fluctuations
3.5 Asymptotically Safe Gravity
3.6 Non-commutative geometry
3.7 Miscellaneous
3.8 Summary of motivations
4 Models and Applications
4.1 Interpretation of a minimal length scale
4.2 Modified commutation relations
4.3 Quantum mechanics with a minimal length scale
4.4 Quantum field theory with a minimal length scale
4.5 Deformed Special Relativity
4.6 Composite systems and statistical mechanics
4.7 Path-integral duality
4.8 Direct applications of the uncertainty principle
4.9 Miscellaneous
5 Discussion
5.1 Interrelations
5.2 Observable consequences
5.3 Is it possible that there is no minimal length?
6 Summary
7 Acknowledgements
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