Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED

TL;DR

This paper proves that for certain translation invariant non-relativistic QED models with net charge, ground states cannot be found within the Fock space, highlighting fundamental limitations of these models.

Contribution

It establishes the non-existence of ground states in the Fock space for a class of translation invariant non-relativistic QED models with net charge, under natural assumptions.

Findings

Ground states do not exist in the Fock space for these models.

The result applies under natural assumptions on the models.

Highlights limitations in the mathematical description of charged quantum systems.

Abstract

We consider a class of translation invariant models of non-relativistic QED with net charge. Under certain natural assumptions we prove that ground states do not exist in the Fock space.