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"Minimal Length Scale Scenarios for Quantum Gravity"

Sabine Hossenfelder

	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	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
	Acknowledgements
	Index
	References
	Footnotes
	Figures
	Tables

The Lorentz group has a second Casimir operator, which is the length of the Pauli–Lubanski pseudovector. It can be identified by it being a function of the angular momentum operator.