Monte-Carlo simulations of abelian projection of T = 0 pure lattice QCD show that 1) Polyakov loops written in terms of abelian link fields alone play a role of an order parameter of deconfinement transition, 2) the abelian Polyakov loops are decomposed into contributions from Dirac strings of monopoles and from photons, 3) vanishing of the abelian Polyakov loops in the confinement phase is due to the Dirac strings alone and the photons give a finite contribution in both phases. Moreover, these results appear to hold good with any abelian projection as seen from the studies in the maximally abelian gauge and in various unitary gauges. *

We investigated the gauge (in)dependence of the connement mechanism due to monopole condensation in SU(2) lattice QCD by various abelian projections. We found (1) the string tension can be reproduced by monopoles alone also in Polyakov gauge and (2) the behaviors of the Polyakov loop at the critical temperature seem to be explained by the uniformity breaking of the monopole currents in every gauge.

We report the preliminary results of the studies of hadron spectrum under the background of abelian and monopole gauge elds in quenched Wilson SU(3) QCD. Abelian gauge elds alone reproduce the same chiral limit as in the full case. Critical hopping parameter c and m are the same in both cases. We need more time to get a denite result in the case of monopole background. The photon contribution do not produce any mass gap in the chiral limit ( = c 0:17). The behavior is similar to those in the free photon case for c = 0:125.

Monte-Carlo simulations of abelian projection in $T \neq 0$ pure lattice QCD show that 1)\ Polyakov loops written in terms of abelian link fields alone play a role of an order parameter of deconfinement transition 2)\ the abelian Polyakov loops are decomposed into contributions from Dirac strings of monopoles and from photons 3)\ vanishing of the abelian Polyakov loops in the confinement phase is due to the Dirac strings alone and the photons give a finite contribution in both phases. Moreover, these results appear to hold good in unitary gauges. This suggests that monopole condensation as the color confinement mechanism is gauge independent.Comment: 3 pages (4 figures). Contribution to Lattice '9

We report the preliminary results of the studies of hadron spectrum under the background of abelian and monopole gauge elds in quenched Wilson SU(3) QCD. Abelian gauge elds alone reproduce the same chiral limit as in the full case. Critical hopping parameter c and m are the same in both cases. We need more time to get a de nite result in the case of monopole background. The photon contribution do not produce any mass gap in the chiral limit ( = c 0:17). The behavior is similar to those in the free photon case for c = 0:125.

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