2006/02/15 by C. Adam, J. Sánchez-Guillén, J. Sanchez-Guillen +4
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th
paper · pdf · doi:10.1063/1.2199089
published as J.Math.Phys.47:052302,2006 · Latex, 35 pages, 1 figure
arxiv created 2006/02/15 · openalex publication_date 2006/05/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study soliton solutions of the Nicole model—a non-linear four-dimensional field theory consisting of the CP1 Lagrangian density to the non-integer power 32—using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behavior to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev–Niemi model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev–Niemi model.