SOLITON-SOLUTIONS OF RELATIVISTIC HARTREE-EQUATIONS

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 m0 interacting both with each other and with themselves via the exchange of a particle of mass mu0. The stationary states of the composite particle are described by relativistic Hartree equations. Since the self-interaction is included, the case of an elementary particle is a non-trivial 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 mu0/m0, while the absolute minimum occurs at mu0 = 0.