Multiplicity of ground states in quantum field models: applications of asymptotic fields

TL;DR

This paper investigates the multiplicity of ground states in quantum field models using asymptotic field theory, providing conditions for finiteness of the number operator's expectation and methods to estimate ground state multiplicity.

Contribution

It introduces a necessary and sufficient condition for the finiteness of the number operator's expectation in ground states and offers a practical method to estimate ground state multiplicity.

Findings

Finite expectation value of the number operator characterized

Method to estimate upper bound of ground state multiplicity

Application to massless GSB and Pauli-Fierz models

Abstract

The ground states of an abstract model in quantum field theory are investigated. By means of the asymptotic field theory, we give a necessary and sufficient condition for that the expectation value of the number operator of ground states is finite, from which we obtain a wide-usable method to estimate an upper bound of the multiplicity of ground states. Ground states of massless GSB models and the Pauli-Fierz model with spin 1/2 are investigated as examples.