From real fields to complex Calogero particles

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.

17 pages, 2 figures

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Cited by in corpus (12)

• PT-symmetric deformations of integrable models
• Bohmian quantum trajectories from coherent states
• PT-symmetry breaking in complex nonlinear wave equations and their deformations
• Antilinear deformations of Coxeter groups, an application to Calogero models
• Non-Hermitian multi-particle systems from complex root spaces
• Deconstructing non-Dirac-hermitian supersymmetric quantum systems
• PT-symmetrically deformed shock waves
• Metric operators for non-Hermitian quadratic su(2) Hamiltonians
• PT-symmetry in quasi-integrable models
• Moduli spaces for PT-regularized solitons
• Calogero-like model without rearrangement symmetry
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models