Free energy from forward scattering in 1+1d

Abstract

The free energy, or equivalently the ground state energy in finite volume, may be calculated from forward scattering amplitudes using a formula due to Dashen, Ma, and Bernstein. However a naive treatment leads to singularities when considering the scattering of three or more particles. It is shown in detail how the approach can be applied to multi-particle scattering in various massive scalar theories in 1+1d, with or without integrability. The results for the sinh-Gordon, Lieb-Liniger, and $O(N)$ non-linear sigma models are compared to exact results. It is shown how bound states can be considered in this approach by considering the attractive Lieb-Liniger model.

41 pages, 8 figures

References in corpus (12)

• The Effective Theory of Long Strings
• Closed flux tubes and their string description in D=2+1 SU(N) gauge theories
• Evidence for a new particle on the worldsheet of the QCD flux tube
• Closed flux tubes and their string description in D=3+1 SU(N) gauge theories
• Flux Tube Spectra from Approximate Integrability at Low Energies
• Introduction to the thermodynamic Bethe ansatz
• Undressing Confining Flux Tubes with $T\bar{T}$
• The Massive Thermal Basketball Diagram
• Looking for Integrability on the Worldsheet of Confining Strings
• Virial expansion and TBA in O(N) sigma models
• Graphical representation of the partition function for a 1-D delta-function Bose gas
• Thermodynamic Bethe Ansatz and Generalised Hydrodynamics in the sine-Gordon model