Monotonicity of the polaron energy II:General theory of operator monotonicity

TL;DR

This paper develops a comprehensive theory of operator monotonicity and applies it to analyze the Fröhlich polaron Hamiltonian, offering a unified perspective on the model's properties.

Contribution

It introduces a general framework for operator monotonicity and demonstrates its application to the Fröhlich polaron Hamiltonian, enhancing theoretical understanding.

Findings

Established a general theory of operator monotonicity.

Applied the theory to the Fröhlich polaron Hamiltonian.

Provided a unified viewpoint of the Fröhlich model.

Abstract

We construct a general theory of operator monotonicity and apply it to the Fr\"ohlich polaron hamiltonian. This general theory provides a consistent viewpoint of the Fr\"ohlich model.