Form factors of descendant operators: Free field construction and reflection relations

Abstract

The free field representation for form factors in the sinh-Gordon model and the sine-Gordon model in the breather sector is modified to describe the form factors of descendant operators, which are obtained from the exponential ones, $\e^{ıαϕ}$, by means of the action of the Heisenberg algebra associated to the field $\varphi (x)$. As a check of the validity of the construction we count the numbers of operators defined by the form factors at each level in each chiral sector. Another check is related to the so called reflection relations, which identify in the breather sector the descendants of the exponential fields $\e^{ıαϕ}$ and $\e^{ı(2α_0-α)ϕ}$ for generic values of $\alpha$. We prove the operators defined by the obtained families of form factors to satisfy such reflection relations. A generalization of the construction for form factors to the kink sector is also proposed.

29 pages; v2: minor corrections, some references added; v3: minor corrections; v4,v5: misprints corrected; v6: minor mistake corrected

References in corpus (3)

• Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory
• On scaling fields in $Z_N$ Ising models
• Form factors of descendant operators in the massive Lee-Yang model

Cited by in corpus (9)

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• On convergence of form factor expansions in the infinite volume quantum Sinh-Gordon model in 1+1 dimensions
• Resonances in sinh- and sine-Gordon models and higher equations of motion in Liouville theory
• Lattice models, deformed Virasoro algebra and reduction equation
• Algebraic approach to form factors in the complex sinh-Gordon theory
• Note on four-particle form factors of operators $T_{2n}{T}_{-2n}$ in sinh-Gordon model
• Semiclassical approach to form factors in the sinh-Gordon model