ALL-ORDERS SKYRMIONS

We consider a special class of Skyrme-like Lagrangians which include higher-order terms in the derivatives of the pion field but leave the degree of the chiral angle equation at 2. Explicit Lagrangians are constructed up to order 24. They are found to be in agreement with a previous conjecture regarding the general form of the static energy density to all orders for the hedgehog solution. In addition, the static energy density gets zero contribution from Lagrangians of order 10, 14, 18, and 22, suggesting that this result extends to all order 4k + 2 for k greater-than-or-equal-to 2. We then proceed to prove both conjectures.