Solutions for the classical sigma model in the hedgehog ansatz

All kinds of solution of the Euler–Lagrange equation obtained from the chiral nonlinear sigma model Lagrangian with the hedgehog ansatz for the SU(2) field are investigated. Making use of the scale invariance of the equation of motion, the solutions are classified in families, according to their analytic properties. It will be shown that the energy integral diverges for all possible classes of solution, and that a finite topological charge can be defined for only one class of solution, and has only one possible numerical value (and its negative).