On three dimensional coupled bosons

TL;DR

This paper investigates a 2+1 dimensional model of two coupled complex scalar fields, demonstrating the potential for bound states of composite particles using bilinear methods within a classical linear approximation.

Contribution

It introduces a new coupled scalar field model in 2+1 dimensions and applies bilinear methods to analyze bound state formation.

Findings

Possible bound states exist for certain coupling strengths.

The classical theory is studied within the linear approximation.

The model differs from previous versions by changing the interaction structure.

Abstract

This is a new version of the paper, which uses the same methods as in the previous version, but the model is now different. We study two complex scalar fields coupled through a quadratic interaction in 2+1 dimensions. We use the method of bilinears as suggested by Rajeev. The resulting classical theory is studied within the linear approximation and we show that there is a possible bound state for the composite type particles for a range of coupling constant strengths.