Exact finite volume expectation values of local operators in excited states

  • B. Pozsgay
  • I. M. Szécsényi
  • G. Takács
Open Access
Regular Article - Theoretical Physics


We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.


Exact S-Matrix Bethe Ansatz Integrable Field Theories 


Open Access

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© The Author(s) 2015

Authors and Affiliations

  1. 1.MTA-BME “Momentum” Statistical Field Theory Research GroupBudapestHungary
  2. 2.Department of Mathematical SciencesDurham UniversityDurhamUnited Kingdom
  3. 3.Institute of Theoretical PhysicsEötvös Loránd UniversityBudapestHungary
  4. 4.Department of Theoretical PhysicsBudapest University of Technology and EconomicsBudapestHungary

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