On the models of Skyrme and Faddeev

Hamiltonians in Magnetic Fields

16 October 15:30 - 16:30

Lev Kapitanski - University of Miami

Both models describe heavy particles (baryons) as spatially localized solutions of PDEs (lumps). In the original Skyrme model, the fields are constant at $|x| = \infty$ maps from $\mathbb R^3$ to the three-dimensional sphere, $S^3$. All such maps are split into different sectors according to their topological charge -- the degree of the map. One of the problems is to minimize the Skyrme energy in every sector. The Faddeev model adds internal structure -- knottedness -- into the lumps. The fields are maps from $\R^3$ into the two-dimensional sphere, $S^2$. The homotopy classes of such maps are characterized by an integer -- the Hopf number, which counts the linking of the pre-images of the regular values. In this talk I will give a (mathematical) review of the two models.
Rafael D. Benguria
Pontificia Universidad Católica de Chile
Arne Jensen
Aalborg University
Georgi Raikov
Pontificia Universidad Católica de Chile
Grigori Rozenblioum
Chalmers/University of Gothenburg
Jan Philip Solovej
University of Copenhagen