Minimization of the Energy of the Non-Relativistic One-Electron Pauli-Fierz Model over Quasifree States

TL;DR

This paper proves the existence and uniqueness of a ground state energy minimizer for a non-relativistic one-electron Pauli-Fierz model within pure quasifree states, under certain physical cutoffs and small parameters.

Contribution

It establishes the existence, uniqueness, and a perturbative expression of the energy minimum for the model within pure quasifree states, extending previous results to this specific setting.

Findings

Existence and uniqueness of the energy minimizer.

Perturbative expression for small momentum and coupling.

Lagrange equation expressed via the generalized one-particle density matrix.

Abstract

In this article is proved the existence and uniqueness of a minimizer of the energy for the non-relativistic one electron Pauli-Fierz model, within the class of pure quasifree states. The minimum of the energy on pure quasifree states coincides with the minimum of the energy on quasifree states. Infrared and ultraviolet cutoffs are assumed, along with sufficiently small coupling constant and momentum of the dressed electron. A perturbative expression of the minimum of the energy on quasifree states for a small momentum of the dressed electron and small coupling constant is then given. We also express the Lagrange equation for the minimizer, in terms of the generalized one particle density matrix of the pure quasifree state.