An Algebraic Approach to Form Factors

Abstract

An associative $\ast$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the algebra automatically satisfies all the form factor axioms. It is argued that this answers the question (posed in the functional Bethe ansatz) how to select the dynamically correct representations of the $TTR$-algebra. Applied to the case of integrable QFTs with diagonal factorized scattering theory a universal formula for the eigenvalues of the conserved charges emerges.

A simplified form of the algebra is used that allows one to dispense with the extra generator C. To appear in Nucl. Phys. B

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• Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model
• Off-Shell Dynamics of the O(3) Nonlinear Sigma-Model -- Beyond Monte-Carlo and Perturbation Theory
• On the boundary form factor program
• The determinant representation for quantum correlation functions of the sinh-Gordon model
• An Algebraic Bootstrap for Dimensionally Reduced Quantum Gravity
• Form Factors, Thermal States and Modular Structures
• The Determinant Representation for a Correlation Function in Scaling Lee-Yang Model
• Two-point correlation functions in perturbed minimal models
• Sequential Bethe vectors and the quantum Ernst system