The multiplicity of the ground state of a generalized particle system interacting with a massless Bose field

TL;DR

This paper investigates a generalized particle system interacting with a massless Bose field, proving that if a ground state exists, its multiplicity must be finite, under certain regularity conditions.

Contribution

It establishes the finiteness of the ground state multiplicity for a broad class of particle-Bose field interactions, extending previous results to more general systems.

Findings

Ground state multiplicity is finite if it exists.

Regularity conditions are crucial for the proof.

The result applies to generalized particle systems with massless Bose fields.

Abstract

A generalized particle system interacting with a massless Bose field is investigated. We assume regularity conditions for the commutation relations of the interaction and annihilation operators. It is proven that if the ground state exists, its multiplicity is finite.