DOCUMENTA MATHEMATICA, Extra Volume ICM III (1998), 183-192

Feodor A. Smirnov

Title: Space of Local Fields in Integrable Field Theory and Deformed Abelian Differentials

In this talk I consider the space of local operators in integrable field theory. This space allows two different descriptions. The first of them is due to conformal field theory which provides a universal picture of local properties in quantum field theory. The second arises from counting solutions to form factors equations. Considering the example of the restricted Sine-Gordon model I show that these two very different descriptions give the same result. I explain that the formulae for the form factors are given in terms of deformed hyper-elliptic integrals. The properties of these integrals, in particular the deformed Riemann bilinear relation, are important for describing the space of local operators.

1991 Mathematics Subject Classification:

Keywords and Phrases:

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