# Hardy and Lieb-Thirring Inequalities for Anyons

@article{Lundholm2013HardyAL, title={Hardy and Lieb-Thirring Inequalities for Anyons}, author={Douglas Lundholm and Jan Philip Solovej}, journal={Communications in Mathematical Physics}, year={2013}, volume={322}, pages={883-908} }

We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter $${\alpha \in [0, 1]}$$α∈[0,1] ranging from bosons (α = 0) to fermions (α = 1). We prove a (magnetic) Hardy inequality for anyons, which in the case that α is an odd numerator fraction implies a local exclusion principle for the kinetic energy of such anyons. From this result, and motivated by Dyson and Lenard’s original approach to the stability of…

## 43 Citations

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