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<p>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 [1]. 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 <i>O</i>(<i>N</i>) 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.</p>

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Free energy from forward scattering in 1+1d

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月3日

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  • Daniel Schubring

摘要

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 [1]. 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.