# Spectral expansion for finite temperature two-point functions and clustering

@article{Szecsenyi2012SpectralEF, title={Spectral expansion for finite temperature two-point functions and clustering}, author={Istv'an M. Sz'ecs'enyi and G'abor Tak'acs}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2012}, volume={2012}, pages={12002} }

Recently, the spectral expansion of finite temperature two-point functions in integrable quantum field theories was constructed using a finite volume regularization technique and the application of multidimensional residues. In the present work, the original calculation is revisited. By clarifying some details in the residue evaluations, we find and correct some inaccuracies of the previous result. The final result for contributions involving no more than two particles in the intermediate… Expand

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#### References

SHOWING 1-10 OF 54 REFERENCES

Diagonal multisoliton matrix elements in finite volume

- Physics
- 2013

We consider diagonal matrix elements of local operators between multi-soliton states in finite volume in the sine-Gordon model, and formulate a conjecture regarding their finite size dependence which… Expand

Finite volume form factors and correlation functions at finite temperature

- Physics
- 2009

In this thesis we investigate finite size effects in 1+1 dimensional integrable QFT. In particular we consider matrix elements of local operators (finite volume form factors) and vacuum expectation… Expand

One-point functions in integrable quantum field theory at finite temperature

- Physics
- 2001

We determine the form factor expansion of the one-point functions in integrable quantum field theory at finite temperature and find that it is simpler than previously conjectured. We show that no… Expand

Form factors in finite volume II: Disconnected terms and finite temperature correlators

- Physics
- 2008

Abstract Continuing the investigation started in a previous work, we consider form factors of integrable quantum field theories in finite volume, extending our investigation to matrix elements with… Expand

Two-point correlation function in scaling Lee-Yang model

- Physics
- 1991

Abstract The structure of the UV singularity in the two-point correlation function is considered for the scaling Lee-Yang model. Both perturbative and nonperturbative corrections to UV conformal… Expand

Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion

- Physics
- 2006

Abstract We propose an approach to the problem of low but finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the… Expand

Form factor perturbation theory from finite volume

- Physics
- 2010

Abstract Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for non-integrable models described as perturbations of… Expand

One-point functions in massive integrable QFT with boundaries

- Physics
- 2010

We consider the expectation value of a local operator on a strip with non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite volume regularisation in the crossed channel and… Expand

Finite temperature correlations in the one-dimensional quantum Ising model.

- Physics
- 1996

Abstract We extend the form-factors approach to the quantum Ising model at finite temperature. The two-point function of the energy is obtained in closed form, while the two-point function of the… Expand

Finite-temperature Dynamical Correlations in Massive Integrable Quantum Field Theories

- Physics
- 2009

We consider the finite-temperature frequency and momentum-dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero-temperature… Expand