Ground States in Non-relativistic Quantum Electrodynamics

TL;DR

This paper proves the existence of true ground states in non-relativistic quantum electrodynamics for all coupling constants and cutoff parameters, including many-particle systems, ensuring a stable lowest-energy state.

Contribution

It establishes the universal existence of ground states in non-relativistic QED models regardless of coupling strength and system complexity, filling a key theoretical gap.

Findings

Ground states exist for all fine-structure constants.

Ground states exist for all ultraviolet cutoffs.

Results apply to many-particle systems under natural conditions.

Abstract

The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the Schr\"odinger equation. We prove quite generally that this state exists for {\it all values} of the fine-structure constant and ultraviolet cutoff. We also show the same thing for a many-particle system under physically natural conditions.