Do anyons solve Heisenberg's Urgleichung in one dimension

Abstract

We construct solutions to the chiral Thirring model in the framework of algebraic quantum field theory. We find that for all positive temperatures there are fermionic solutions only if the coupling constant is $\lambda =\sqrt{2(2n+1)\pi },n\in \mathbf{N}$.

19 pages LaTeX, to appear in Eur. Phys. J. C

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