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It is shown that the scattering amplitude for contact-interacting anyons does exhibit a genuine non-perturbative sector. This means that the corresponding perturbative field theoretical formulation, based on the 2+1 non-relativistic Chern-Simons gauge model coupled to self-interacting complex scalar field, is not generally able to reproduce, order by order in perturbation theory, the exact result...
An exact expression for the Green function of a purely fermionic system moving on the manifold RxΣ D-1 , where Σ D-1 is a (D-1)-torus, is found. This expression involves the bosonic analog of χ n =e inθ corresponding to the irreducible representation for the nth class of homotopy and in the fermionic case for D=2 and 3, χ n is a...
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