Gauge-invriant quasi-free states on the algebra of the anyon commutation relations

Eugene Lytvynov

Let $X={\mathbb{R}}^2$ and let $q\in \mathbb{C}$, $|q|=1$. For $x=(x^1,x^2)$ and $y=(y^1,y^2)$ from $X^2$, we define a function $Q(x,y)$ to be equal to $q$ if $x^1<y^1$, to $\bar{q}$ if…