
Abstract 
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 
Noncommutative 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 
Pathintegral 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 

Index 

References 

Footnotes 

Figures 

Tables 