We formulate a stochastic gauge fixing method to study the gauge dependence of the Abelian projection. We consider a gauge which interpolates between the maximal Abelian gauge and no gauge fixing. We have found that Abelian dominance for the heavy quark potential holds even in a gauge which is far from maximally Abelian one. The heavy quark potentials from monopole and photon contribution are calculated at several values of the gauge parameter, and the former part shows always the confinement behavior.

We calculate inter-meson potentials numerically by solving classical equations of motion derived from Dual Ginzburg-Landau (DGL) Theory. Inter-meson potentials in DGL theory are shown to be similar to those of the stringflip model and well reproduce behaviors of the short-range interaction at the classical level. We also compare our results with those from lattice QCD Monte carlo calculations. †

The chiral phase structure of the Nambu-Jona-Lasinio/Gross-Neveu model at finite temperature T and finite chemical potential µ is investigated using the (Wilsonian) nonperturbative renormalization group (NPRG). In the large N c limit, the solutions of NPRG with various cutoff schemes are given. For a sufficiently large ultraviolet cutoff, the NPRG results coincide with those of the Schwinger-Dyson equation and have little cutoff scheme dependence. Next, to improve the approximation, we incorporate the mesonic fluctuations. We introduce the auxiliary fields for mesons and then derive NPRG equation for finite N c . The chiral phase structure on the (T, µ) plane beyond the leading order of the 1/N c expansion is investigated in the sharp cutoff limit. The N c dependence of the chiral phase diagram is obtained. * ) In § 3, we employ this smooth cutoff regularization to see the cutoff scheme b (in)dependence. For an infinitesimal neighborhood of the fixed point, this linearization is valid. * * ) I( T , 0) is like an approximation of the integral I 0 using a histogram whose band width is 2π T . Because the trapezoidal-rule estimate differs from the integral by the quantity on the order of the square of the width, 22) I( T , 0) also differs from I 0 by O( T 2 ). * * * ) By dimensional analysis, T c is independent of Λ 0 .

Three topics concerning infrared effective lattice QCD are discussed. (1)Perfect lattice action of infrared SU (3) QCD and perfect operators for the static potential are analytically given when we assume two-point monopole interactions alone. The assumption seems to be justified from numerical analyses of pure SU (3) QCD in maximally abelian gauge. (2)Gauge invariance of monopole dominance can be proved theoretically if the gauge invariance of abelian dominance is proved. The gauge invariance of monopole condensation leads us to confinement of abelian neutral but color octet states after abelian projection. (3)A stochastic gauge fixing method is developed to study the gauge dependence of the Abelian projection, which interpolates between the maximally abelian (MA) gauge and no gauge fixing. Abelian dominance for the heavy quark potential holds even in the gauge which is far from Maximally Abelian one.