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arXiv:0912.1149 · Journal of Physics A Mathematical and Theoretical

A vertex operator approach for form factors of Belavin's ({\mathbb Z}/n{\mathbb Z})-symmetric model

Yas-Hiro Quano

Published Feb 4, 2010• 3 citations
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Abstract

Belavin's -symmetric model is considered on the basis of bosonization of vertex operators in the A (1) n − 1 model and vertex-face transformation. Free-field representations of nonlocal tail operators are constructed for off-diagonal matrix elements with respect to the ground state sectors. As a result, integral formulae for form factors of any local operators in the -symmetric model can, in principle, be obtained.

DOI
10.1088/1751-8113/43/8/085202

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The process of using the free field representation to construct form factors of two dimensional integrable models is very promising. In this thesis, this procedure is analysed and adapted for application to the chiral Gross-Neveu model. The vertex operators and Zamolodchikov-Faddeev algebra for the particles are presented, with a similar structure producing a representation of the local operators of the theory. Using these techniques, the form factors of the model are then constructed as traces over the space of Zamolodchikov-Faddeev operators, and given in terms of an integral representation. In particular, the two-particle form factors of the current operator are found, and shown to agree with previous results in the literature.