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

TL;DR

This work analyzes the ground-state multiplicity for a generalized particle system coupled to a massless Bose field under a comprehensive set of regularity conditions. The authors develop a proof framework that combines momentum localization with a boson-derivative bound, centered on a Pull-Through Formula, to show that any existing ground state cannot be infinitely degenerate. The main theorem asserts that, under conditions (H1)–(H10), the multiplicity of the ground state ker(H − E0(H)) is finite, independent of the coupling strength, and applies to explicit models such as the Wigner-Weisskopf model and a lattice spin system. This result provides structural insight into the spectral properties of massless field models and supports stability analyses in quantum field theoretic settings.

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.

Theorems & Definitions (8)

• Theorem 1.1
• Proposition 2.1
• Lemma 2.2
• Proposition 2.3
• Lemma 2.4
• Proposition 2.5
• Corollary 2.6
• Theorem 3.1