Approaches to form-factors of higher spin Heisenberg chains
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In this thesis we apply the vertex operator approach of Jimbo and Miwa to higher spin Heisenberg chains with the aim of computing the form-factors of these quantum integrable models. The work is motivated by the relation of the form-factors to the dynamical structure factors of the model - objects that are experimentally realisable - and potential for comparison with real-world results. Using a one boson, one fermion free field realisation of Uq(sl2), in conjunction with a realisation for the fermionic contribution due to Shiraishi, we are able to give the formalism required to obtain explicit multiple integral expressions for the 2m-particle form-factors of the antiferromagnetic spin-1 Heisenberg chain. Using this novel boson-fermion-Shiraishi scheme, we are able to obtain single integral expressions for the two-spinon contribution to the S+ form-factor. We also consider a certain modification of a known q-Wakimoto bosonisation scheme for arbitrary spin and its relevance to the computation of higher spin form-factors. We consider the form of the resultant BRST relations and discuss simplifications arising through this approach, as well as the difficulties faced in obtaining integral expressions.