Infrared divergence of a scalar quantum field model on a pseudo Riemannian manifold

TL;DR

This paper investigates the infrared divergence phenomena in a scalar quantum field model on a pseudo Riemannian manifold, showing that short-range variable mass leads to no ground state and analyzing boson expectation divergence.

Contribution

It introduces a unitarily transformed scalar quantum field model with variable mass and demonstrates the absence of a ground state under short-range mass conditions.

Findings

Hamiltonian has no ground state with short-range variable mass

Infrared divergence affects expectation values of boson number

Use of Feynman-Kac-type formula to analyze the model

Abstract

A scalar quantum field model defined on a pseudo Riemann manifold is considered. The model is unitarily transformed the one with a variable mass. By means of a Feynman-Kac-type formula, it is shown that when the variable mass is short range, the Hamiltonian has no ground state. Moreover the infrared divergence of the expectation values of the number of bosons in the ground state is discussed.