Physics – Mathematical Physics
Scientific paper
2009-07-05
Physics
Mathematical Physics
34 pages, no figures
Scientific paper
We study geometric variational problems for a class of nonlinear sigma-models in quantum field theory. Mathematically, one needs to minimize an energy functional on homotopy classes of maps from closed 3-manifolds into compact homogeneous spaces G/H. The minimizers are known as Hopfions and exhibit localized knot-like structure. Our main results include proving existence of Hopfions as finite energy Sobolev maps in each (generalized) homotopy class when the target space is a symmetric space. For more general spaces we obtain a weaker result on existence of minimizers in each 2-homotopy class. Our approach is based on representing maps into G/H by equivalence classes of flat connections. The equivalence is given by gauge symmetry on pullbacks of G-->G/H bundles. We work out a gauge calculus for connections under this symmetry, and use it to eliminate non-compactness from the minimization problem by fixing the gauge.
Koshkin Sergiy
No associations
LandOfFree
Gauge theory of Faddeev-Skyrme functionals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Gauge theory of Faddeev-Skyrme functionals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gauge theory of Faddeev-Skyrme functionals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-27061