Soliton solutions of relativistic Hartree equations

DOI10.1088/0305-4470/26/14/023zbMATH Open0795.35095arXivhep-th/9305035OpenAlexW1983787756MaRDI QIDQ4290762

Publication date: 25 September 1994

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: We study a model based on

N

scalar complex fields coupled to a scalar real field, where all fields are treated classically as c-numbers. The model describes a composite particle made up of

N

constituents with bare mass

m_{0}

interacting both with each other and with themselves via the exchange of a particle of mass

m u_{0}

. The stationary states of the composite particle are described by relativistic Hartree's equations. Since the self-interaction is included, the case of an elementary particle is a nontrivial special case of this model. Using an integral transform method we derive the exact ground state solution and prove its local stability. The mass of the composite particle is calculated as the total energy in the rest frame. For the case of a massless exchange particle the mass formula is given in closed form. The mass, as a function of the coupling constant, possesses a well pronounced minimum for each value of

m u_{0} / m_{0}

, while the absolute minimum occurs at

m u_{0} = 0

.

Full work available at URL: https://arxiv.org/abs/hep-th/9305035

zbMATH Keywords

integral transform method mass formula self-interacting system exact ground-state solution

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Many-body theory; quantum Hall effect (81V70) PDEs in connection with relativity and gravitational theory (35Q75)

Related Items (7)

Semiclassical soliton-type solutions of the Hartree equation ⋮ Intertwining solutions for magnetic relativistic Hartree type equations ⋮ Vortex solutions for pseudo-relativistic Hartree equations ⋮ On radial solutions of semi-relativistic Hartree equations ⋮ Quasiclassical soliton solutions of the Hartree equation. Newtonian interaction with screening ⋮ Dynamics of relativistic solitons due to pseudo Sine-Gordon equation ⋮ The unified approach to integrable relativistic equations: Soliton solutions over nonvanishing backgrounds. II

This page was built for publication: Soliton solutions of relativistic Hartree equations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4290762)