Abstract
Using the fermionic basis we conjecture exact expressions for diagonal finite volume matrix elements of exponential operators and their descendants in the sinh-Gordon theory. Our expressions sum up the LeClair-Mussardo type infinite series generalized by Pozsgay for excited state expectation values. We checked our formulae against the Liouville three-point functions for small, while against Pozsgay's expansion for large volumes and found complete agreement.
Highlights
Integrable models are ideal testing grounds of various methods and ideas in quantum field theories
The LeClair-Mussardo formula [18] provides an infinite series for the exact finite volume one-point function, where each term contains the contribution of a given number of virtual particles in terms of their infinite volume connected form factors and a weight function, which is related to the Thermodynamic Bethe ansatz (TBA) densities of these particles [19]
The linear integral equation contains a measure, which is built up from the pseudo-energy of the excited state TBA equations and a kernel, which is a deformation of the TBA kernel
Summary
Integrable models are ideal testing grounds of various methods and ideas in quantum field theories. The LeClair-Mussardo formula [18] provides an infinite series for the exact finite volume one-point function, where each term contains the contribution of a given number of virtual particles in terms of their infinite volume connected form factors and a weight function, which is related to the Thermodynamic Bethe ansatz (TBA) densities of these particles [19] This formula was generalized by analytical continuation for diagonal matrix elements, which replaces. There have been active work and relevant progress in deriving finite volume one-point functions for the exponential operators and their descendants in these theories [23, 24] These results were extended for diagonal matrix elements in the sine-Gordon theory [25, 26, 27] and the aim of our paper is to provide similar expressions in the sinh-Gordon theory.
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