  In-medium sum rules following from the chiral charge algebra of QCD are
reviewed, and new sum rules are derived. The new sum rules relate the
I^G(J^{PC})=1^-(0^{++}) excitations (quantum numbers of a_0(980)) to the scalar
and isovector densities, and are nontrivial for the isospin-asymmetric medium.
We present an extensive illustration of the sum rules with help of quark matter
in the Nambu-Jona--Lasinio model. Collective excitations different from the
usual meson branches (spin-isospin sound modes) are shown to contribute
significantly to the sum rules and to play a crucial role in the limit of
vanishing current quark masses.
