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Seminar Abstracts
Lev Kapitanski, Department of Mathematics, Kansas State University."Holonomy and Skyrme's model" Abstract The Skyrme model (1961) was one of the first attempts to describe
elementary particles as localized in space solutions of nonlinear
PDEs. The fields take their values in In this talk I will discuss the existence of minimizers for the Skyrme
energy functional. Also, I will consider two generalizations of the
Skyrme model: one is a variational problem for maps from a compact TUESDAY, November 18, 2003 |
and stabilize at
spatial infinity. Thus, the configuration space splits into different
sectors (homotopy classes) with a constant topological charge (the
degree) in each sector. 
-manifold to a compact Lie group; the other is a variational
problem for flat connections. I will describe the path components of
the configuration spaces of smooth fields for each of the variational
problems. The invariants separating the path components are the
Chern-Simons invariant and a holonomy representation. It turns out
that the Chern-Simons invariant is well defined for connections with
finite Skyrme energy. As for holonomy, we have to define it in such a
way that the definition is valid for distributionally flat 
connections. In particular, our definition is valid
for flat connections with bounded Skyrme energy. The key analytical
result here is a nonlinear Poincaré lemma.