Dyson expansion for form-bounded perturbations and applications to the polaron problem
Abstract
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 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.
Fields of Study & Subjects
Random Matrices and Applications
Stochastic processes and statistical mechanics
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Letters in Mathematical Physics
- Volume
- 116
- Issue
- 4
- Publication date
- 17 July 2026
- Language
- EN