Unusual Bound States in QFT Models

TL;DR

This paper investigates the relativistic bound states in the Wick-Cutkosky model, revealing small attraction effects, critical coupling thresholds for discrete levels, and the nature of states with positive and negative norms.

Contribution

It demonstrates the existence of relativistic bound states with discrete levels and analyzes the norm signatures, clarifying their physical relevance in the Bethe-Salpeter framework.

Findings

Small attraction between like-charged particles due to relativistic effects

Discrete levels emerge when coupling exceeds critical values

Negative norm states can be excluded from the physical sector

Abstract

Homogeneous Bethe-Salpeter equation for simplest Wick-Cutkosky model is studied in the case when the mass of the two-body system is more then the sum of constituent particles masses. It is shown that there is always a small attraction between the like-sigh charged particles as a pure relativistic effect. If the coupling constant exceeds some critical values there arise discrete levels.The situation here is analogous to the so-called "abnormal" solutions.The signature of the norm of these discrete states coincides with the "time-parity".The states with the negative norms can be excluded from the physical sector-the one-time (quasipotential) wave-function corresponding to them vanishes identically.However the positive norm states survive and contribute to the total Green function (and the S-matrix) with the proper sign.