Finite-Temperature Form Factors: a Review

Abstract

We review the concept of finite-temperature form factor that was introduced recently by the author in the context of the Majorana theory. Finite-temperature form factors can be used to obtain spectral decompositions of finite-temperature correlation functions in a way that mimics the form-factor expansion of the zero temperature case. We develop the concept in the general factorised scattering set-up of integrable quantum field theory, list certain expected properties and present the full construction in the case of the massive Majorana theory, including how it can be applied to the calculation of correlation functions in the quantum Ising model. In particular, we include the ''twisted construction'', which was not developed before and which is essential for the application to the quantum Ising model.

This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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• Non-Equilibrium Dynamics and Weakly Broken Integrability
• Generalized hydrodynamics regime from the thermodynamic bootstrap program
• Form factors and generalized hydrodynamics for integrable systems
• Sine-Gordon form factors in finite volume
• Spectral expansion for finite temperature two-point functions and clustering
• Entanglement Content of Quantum Particle Excitations III. Graph Partition Functions
• Diagonal multi-soliton matrix elements in finite volume
• Sine-Gordon multi-soliton form factors in finite volume
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• Effective free-fermionic form factors and the XY spin chain
• Exact large-scale fluctuations of the phase field in the sine-Gordon model
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Inelastic decay from integrability
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Relaxation dynamics of integrable field theories after a global quantum quench
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• A diagrammatic approach towards the thermodynamics of integrable systems
• Mixed-state form factors of $U(1)$ twist fields in the Dirac theory
• Dynamical correlation functions in the Ising field theory