Color Superconductivity For High Density Nuclear Matter

In this paper we built the relation between the thermodynamical theory of the phase transition and fields theory. We emphasized that in the quantum field theory we have to introduce the order parameter fields. Then the discussion of the phase transition is closed to the creation of the Goldstone bosons. If we only discuss the first order transition, the Goldstone bosons fields are sufficient. If we want to discuss the second order transition, we have to discuss a set of fields which constructs a representation of a symmetry group. We also apply this concept to color superconductivity.In charper one, we introduce the international new research about color condensate. The behavior of matter at high quark density is interesting in itself and is relevant to phenomena in the early universe, in neutron star, and in heavy-ion collision. The diquark condensate can't be color singlet. So the color symmetry is broken. This is similar to electric superconductivity. So it is called color superconductivity. The diquark condensate is different to condensate. In the condition of low density and low energy, the < q q > condensate must occur. So the energy value of vacuum can be the lowest one. But the color superconductivity can't be broken. So the diquark condensate can't occur. When the density is hiqh, the color and chiral symmetry will be broken. So the diquark condensate will occur.Up to now, the main techniques for studying the nonperturbative aspectsof QCD are lattice gauge theory[22], QCD sum rules[23], the instanton approximation[24], and some other approaches. They have achieved brilliant success in describing different characteristics of low-energy QCD. On the other hand, phenomenological models such as the MIT bag model[25], chiral bag model[26], topological-soliton model[27], Bethe-Salpeter(BS) equation approximation[28], etc, have also been quite successful in depicting the properties of hadrons.In charper two,we define the phase-transition. A first order phase transition is a point across which some thermodynamic variables(the density of a fluid, or the magnetization of a ferromagnet)changes discontinuously. These discontinuously changed quantities are called order parameters. In most circumstances, it is possible to change a second dynamical quantity in such a way that the competing states move closer together and two states become identical. Then the discontinuity in the order parameter disappears. This endpoint is called critical point.The effective potential V is defined by T= vV. Where v is the four dimensional volume. The nonzero solution of the stable point of V spontaneously breaks the symmetry. We can show that for each generator which is broken there is a massless boson called goldstone.The objects of the study are the many electrons and electro-magnetic fields. Because of the interaction, the cooper's pairs form in superconductor. In the field theory we have to introduce the cooper's pairs field as order parameter field. In the superconductor phase the vacuum expectation of the field operator of cooper's pairs has nonzero value. This breaks U(l) symmetry. Consequently the electromagnetic gauge invariance is spontaneously broken. Analogy the electric superconductivity, we can deal with the color superconductivity.We have known that the superconductivity is related to forming of the fermion pairs. According to the previous discussion the system of high quark density can be described by a field theory. In the effective action we can study local and nonlocal condensates. The GCM bilocal fields is a very excellent way to deal with this case.