From real fields to complex Calogero particles

TL;DR

This paper introduces a new method to derive complex PT-symmetric multi-particle Calogero systems from real nonlinear field equations, revealing how singularities can be interpreted as interacting complex particles.

Contribution

It presents a novel procedure for generating complex Calogero systems from real equations, expanding the understanding of PT-symmetry in multi-particle quantum models.

Findings

Derived new complex PT-symmetric Calogero systems.

Interpreted wave singularities as complex particle interactions.

Analyzed two- and three-particle scattering phenomena.

Abstract

We provide a novel procedure to obtain complex PT-symmetric multi-particle Calogero systems. Instead of extending or deforming real Calogero systems, we explore here the possibilities for complex systems to arise from real nonlinear field equations. We exemplify this procedure for the Boussinesq equation and demonstrate how singularities in real valued wave solutions can be interpreted as N complex particles scattering amongst each other. We analyze this phenomenon in more detail for the two and three particle case. Particular attention is paid to the implemention of PT-symmetry for the complex multi particle systems. New complex PT-symmetric Calogero systems together with their classical solutions are derived.