Reterenees.~lb Stra ci:Nontopolugical solitons are stable hounu state solutions whose boundary condition at infinity is the same as that for the phssical vacuum state. They exist in classical, as well as quantum mechanical, field theories.. These solutmoits in ans space-dimension are rcs iewed. We also discuss their applications to Bose liquid, hadron structures and soliton stars, 'Ibis research ssas supported in part by the US Department of Energs f)37(f-1S73:92/$lS.0() © 1992 Elsevier Science Publishers B.V. All rights reserved 253 2~4 1'. I). /,i'i' said I . /'any' , Nontopologu al so/ito,p rocess. Some general discussions are given in section 3. 1, stability under small perturbations is shown in section 3.2, and quantization in section 3.3.It is generally believed that QCD is the correct theory for the strong interaction and that eventually the detailed hadronic structure will he calculated from QCD. In the high energy region, because of asymptotic freedom, perturbation expansion is valid. This enables us to deduce many parameters for the quarks from high energy experiments. But in the low energy region. where it is of importance to the hadronic structure, the theory cannot be solved perturbatively. and nonperturhative effects dominate. The origin of quark confinement remains a major theoretical difficulty. For practical calculations. phenomenological models have been built to take into account some of the nonperturbative effects. SO that the rest of the theory can be solved by a perturbative method. As an application of nontopological solitons, section 5 discusses the Friedberg-Lee model. There are two very good reviews on this model and its variations. One is the volume "Nontopological Solitons" by Wilets [20], the other is a review article by Birse 1211. Here we will give a summary of major results.Another application of nontopological solitons is in exotic stellar structures, called soliton stars [24-27] to be discussed in section 6. Stable cold stellar configurations have been found which can have masses up to that of a galaxy. Soliton stars can he made either of boson fields or fermion fields. Their characteristics depend sensitively on nonlinear couplings. These stellar configurations all have energies lower than the corresponding free particle (plane wave) solution for any given particle number; consequently. soliton stars are prevented from decaying into free particles.. When a soliton star exceeds a certain critical mass, it collapses into a black hole. Because the mechanism for stability is quite different between soliton stars and ordinary stars, the soliton stars can have very different critical masses [7, 8,24,28] from the usual Oppenheimer-Volkov [29] type limit.Recently, the nontopological soliton has been extended to the study of the Bose liquid [30]. The liquid-gas phase transition can be formulated in terms of the spontaneous symmetry breaking of translational invariance in the canonical ensemble, while the Bose-Einstein transition is due to the breaking of the phase symmetry of the complex...

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