Non-commutative Lévy processes for generalized (particularly anyon) statistics

Marek Bozejko, Eugene Lytvynov, Janusz Wysoczanski

Let $T={\mathbb{R}}^d$. Let a function $Q:T^2\to \mathbb{C}$ satisfy $Q(s,t)=\overline{Q(t,s)}$ and $|Q(s,t)|=1$. A generalized statistics is described by creation operators ${\partial }_t^{†}$ a…