On exact solutions of the nonlinear Heisenberg–Klein–Gordon equation in a space–time of constant spacelike curvature

Abstract

A nonlinear complex scalar field theory associated with a ’’squared’’ Heisenberg–Pauli–Weyl nonlinear spinor equation is considered. In a d+1 dimensional universe of constant spatial curvature exact localized solutions for the resulting [‖φ‖2d/(d−2)−const ‖φ‖2(d−1)/(d−2)] model are constructed. For ’’soliton-like’’ solutions with quantized (nontopological) charge the field energy and the Heisenberg uncertainty principle are analyzed.