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<p>We present an abstract Dyson expansion for perturbations that are merely relatively form-bounded, and apply it to the polaron problem. For a large class of polaron-type models, including the Fröhlich and Nelson models, we prove that the vacuum expectation value of the heat semi-group is a completely monotone function of the square of the total momentum. Consequently, the ground-state energy is a concave function of the square of the momentum, a result recently proved for the Fröhlich model in [14] using a probabilistic approach via Wiener integrals.</p>

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Dyson expansion for form-bounded perturbations and applications to the polaron problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月17日

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  • Davide Desio,
  • Robert Seiringer

摘要

We present an abstract Dyson expansion for perturbations that are merely relatively form-bounded, and apply it to the polaron problem. For a large class of polaron-type models, including the Fröhlich and Nelson models, we prove that the vacuum expectation value of the heat semi-group is a completely monotone function of the square of the total momentum. Consequently, the ground-state energy is a concave function of the square of the momentum, a result recently proved for the Fröhlich model in [14] using a probabilistic approach via Wiener integrals.