Intuitive Understanding

The Goldstone model static solutions onS1

“…In particular, we explicitly demonstrated this fact for the normal modes around the type-I solutions. As one varies the parameter L to approach the bifurcation point L = N along the type-I solution with winding N , the correct spectrum is the one which coincides with that of the main branch (4).…”

“…The purpose of this note is to present the complete list of static classical solutions of the Goldstone model on S 1 , the corresponding bifurcation tree and their stability properties. This analysis, apart from its own mathematical interest [4], may provide insight useful in our search for stable solitons in the 2HSM or in the special case of the minimal supersymmetric standard model.…”

Antiperiodic solitons of the Goldstone model onS1

“…This solution is called type I. One can observe that the above solution reduces to (8) when L = N + 1/2, i.e. when one of the ω of equation ( 9) crosses zero.…”

“…for some integer m. When we reach the limit of k → 0 (i.e. L → m + 1 2 ) the solution ( 13) approaches (8). The energy of the above solution is given by the integral…”

“…We also check the case of mixed boundary conditions and place a note with our conclusions in the end. The following analysis is of interest both in mathematical [8] and physical contexts, as it can be useful for the search of stable solitons in the two-Higgs standard model (2HSM) or the minimal supersymmetric standard model.…”