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arXiv · 2512.13443

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

Davide Desio·Robert Seiringer
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Abstract

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 Fr\"ohlich 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 Fr\"ohlich model in \cite{polzer} using a probabilistic approach via Wiener integrals.

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Davide Desio, Robert Seiringer. 2025-12-15. Dyson expansion for form-bounded perturbations and applications to the polaron problem. https://doi.org/10.1007/s11005-026-02107-2

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