On the finite volume expectation values of local operators in the sine-Gordon model

Abstract

In this paper we present sets of linear integral equations which make possible to compute the finite volume expectation values of the trace of the stress energy tensor ($\Theta$) and the $U(1)$ current ($J_{\mu }$) in any eigenstate of the Hamiltonian of the sine-Gordon model. The solution of these equations in the large volume limit allows one to get exact analytical formulas for the expectation values in the Bethe-Yang limit. These analytical formulas are used to test an earlier conjecture for the Bethe-Yang limit of expectation values in non-diagonally scattering theories. The analytical tests have been carried out upto three particle states and gave agreement with the conjectured formula, provided the definition of polarized symmetric diagonal form-factors is modified appropriately. Nevertheless, we point out that our results provide only a partial confirmation of the conjecture and further investigations are necessary to fully determine its validity. The most important missing piece in the confirmation is the mathematical proof of the finiteness of the symmetric diagonal limit of form-factors in a non-diagonally scattering theory.

54 pages

References in corpus (12)

• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Quantum quench in the sine-Gordon model
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Finite-temperature lineshapes in gapped quantum spin chains
• HHL correlators, orbit averaging and form factors
• String field theory vertex from integrability
• Overlap singularity and time evolution in integrable quantum field theory
• Luscher's mu-term and finite volume bootstrap principle for scattering states and form factors
• Quantum quench in the attractive regime of the sine-Gordon model
• Diagonal multi-soliton matrix elements in finite volume
• Exact finite volume expectation values of $\bar{\Psi }\Psi$ in the Massive Thirring model from light-cone lattice correlators
• Lattice approach to finite volume form-factors of the Massive Thirring/Sine-Gordon model

Cited by in corpus (3)

• Diagonal finite volume matrix elements in the sinh-Gordon model
• The LeClair-Mussardo series and nested Bethe Ansatz
• One point functions of fermionic operators in the Super Sine Gordon model