Non-trivial Behaviour of the Scattering Amplitude of Contact-interacting Anyons

Details Non-trivial Behaviour of the Scattering Amplitude of Contact-interacting Anyons Non-trivial Behaviour of the Scattering Amplitude of Contact-interacting Anyons

1997-06-27

arxiv.org/abs/hep-th/9706198v2

Phys.Lett. B441 (1998) 257-264

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, TeX, no figures. Revised version to appear on Phys. Lett. B

Scientific paper

10.1016/S0370-2693(98)01155-1

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 {\it 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. It is proven that the full agreement between the exact scattering amplitude and the resummation of the perturbative expansion of the renormalized 1PI amplitude actually occurs only for some continuous sub-family of self-adjoint extensions of the quantum Hamiltonians, which entail the absence of bound states. A comparison with previously obtained results is carefully worked out.

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