Towards the Construction of Wightman Functions of Integrable Quantum Field Theories

Abstract

The purpose of the ``bootstrap program'' for integrable quantum field theories in 1+1 dimensions is to construct a model in terms of its Wightman functions explicitly. In this article, this program is mainly illustrated in terms of the sine-Gordon and the sinh-Gordon model and (as an exercise) the scaling Ising model. We review some previous results on sine-Gordon breather form factors and quantum operator equations. The problem to sum over intermediate states is attacked in the short distance limit of the two point Wightman function for the sinh-Gordon and the scaling Ising model.

arXiv commentLATEX 18 pages, Talk presented at the '6th International Workshop on Conformal Field Theories and Integrable Models', in Chernologka, September 2002

References in corpus (8)

• Exact expectation values of local fields in quantum sine-Gordon model
• Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model
• On the Operator Content of the Sinh-Gordon Model
• Asymptotic factorisation of form factors in two-dimensional quantum field theory
• Exact form factors in integrable quantum field theories: the sine-Gordon model (II)
• Angular quantization and form-factors in massive integrable models
• Stress-Energy Tensor and Ultraviolet Behaviour in Massive Integrable Quantum Field Theories
• M(atrix) String Theory on K3

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