Chiral Restoration and the Scalar and Vector Correlations in Hot and Dense Matter

First, it is pointed out that hadron/nuclear physics based on QCD should beregarded as ``condensed matter physics'' of the QCD vacuum. We indicate thatphase shift analyses which respect chiral symmetry (ChS), analyticity andcrossing symmetry of the scattering amplitude show the $\sigma$ meson pole inthe s-channel in the low mass region as well as the $\rho$ meson pole in the$t$-channel in the \pipi scattering in the scalar channel. We review recentdevelopments in exploring possible precursory phenomena of partial restorationof \chis in nuclear medium by examining the spectral function in the scalar andthe vector channels. We emphasize that the wave function renormalization of thepion in the medium plays an essential role to induce the decrease of the piondecay constant as the order parameter of chiral transition. An emphasis is alsoput on the importance to examine the scalar and vector channels simultaneouslyfor exploring the possible restoration of chiral symmetry.Comment: talk presented at the YITP-RCNP Workshop on Chiral Restoration in Nuclear Medium (October 7-9, 2002