SUMMING SKYRMIONS

The Skyrme model has the same high-density behaviour as a free quark gas. However, the inclusion of higher-order terms spoils this agreement. We consider the all-order sum of a class of chiral invariant lagrangians of even order in L-mu suggested by Marleau. We prove Marleau's conjecture that these terms are of second order in the derivatives of the chiral angle for the hedgehog case and show that the terms are unique under the additional condition that, for each order, the identity map of the 3-sphere S3(L) is a solution. The general form of the summation can be restricted by physical constraints leading to stable results. Under the assumption that the lagrangian scales like the non-linear sigma model at low densities and like the free quark gas at high densities, we prove that a chiral phase transition must occur.