Rajeev - Physics

The Skyrme TermSkyrme’s ideas was to add a term that violated the abovescaling, which would stabilize the static solution.εS = 1 2g ij ∂ µ φ i ∂ ν φ j η µν√ −ηdx+g ij g kl ∂ µ φ i ∂ ν φ j ∂ ρ φ k ∂ σ φ l [η µρ η νσ − η µσ η νρ ] √ −ηdxThe last term is a short-range repulsion. There are now staticsolutions of winding number one.Is it now true that smooth initial data will remain smoothforever?This is the regularity question I asked Christodoulu.Once we have a regularity theory for the wave map, we areready to tackle this question for the Skyrme model.For simplicity consider only the equivariant case (sphericallysymmetric or hedgehog configurations) U(x,t)=e iσ·ˆxu(r,t)S. G. Rajeev Progress on the Skyrme Model