Soliton matter

Although quantum chromodynamics is generally accepted as the fundamental theory of the strong interactions, there exist no solutions to the theory which describe the binding of quarks to form the observed particles of nuclear physics. Soliton bag models of hadronic matter attempt to capture the main features of quark confinement, while remaiing amenable to calculation. In the context of the non-topological soliton model, nuclear matter is regarded as a collection of quark clusters arranged on a regular lattice in bag-like soliton structures. The conjectured phase transition of nuclear matter to quark plasma at high densities is then modelled as the melting of the soliton crystal under compression. This paper reviews some recent results on multi-soliton solutions of the linear sigma model in one space and one time dimension. Remarkably, exact periodic soliton solutions can be derived in terms of complete Jacobi elliptic integrals for arbitrarily large lattices. The conditions for a phase transition in the model, and implications for more realistic calculations are discussed. 16 refs., 8 figs