A "toy" model in QFT with no lower bound to the energy

TL;DR

This paper presents a simplified quantum field theory model demonstrating that interacting fields can lack a lower energy bound, challenging the common assumption of a stable vacuum state.

Contribution

It introduces a toy model of interacting scalar fields showing the absence of a lower energy bound, which questions standard assumptions in quantum field theory.

Findings

No lower energy bound in the proposed model

Interacting fields can destabilize the vacuum energy

Challenges the assumption of a stable vacuum in QFT

Abstract

In quantum field theory, it is generally assumed that there is a lower bound to the energy, which is normally assumed to the the vacuum state. While this may be a reasonable assumption for a free field it is not necessarily the case for interacting fields. In this paper I will examine a "toy" model of a neutral scalar field interacting with a charged scalar field and show that there is no lower bound to the energy in this case.