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 be regarded as 'condensed matter physics' of the QCD vacuum. We indicate that phase shift analyses which respect chiral symmetry (ChS), analyticity and crossing symmetry of the scattering amplitude show the σ meson pole in the s-channel in the low mass region as well as the ρ meson pole in the t-channel in the π-π scattering in the scalar channel. We review recent developments in exploring possible precursory phenomena of partial restoration of ChS in nuclear medium by the examining spectral function in the scalar and the vector channels. We emphasize that the wave function renormalization of the pion in the medium plays an essential role to induce the decrease of the pion decay constant as the order parameter of chiral transition. An emphasis is also put on the importance to examine the scalar and vector channels simultaneously for exploring the possible restoration of chiral symmetry. (author)