  We consider sum rules of the Weinberg type at zero and nonzero temperatures.
On the basis of the operator product expansion at zero temperature we obtain a
new sum rule which involves the average of a four-quark operator on one side
and experimentally measured spectral densities on the other. We further
generalize the sum rules to finite temperature. These involve transverse and
longitudinal spectral densities at each value of the momentum. Various
scenarios for the relation between chiral symmetry restoration and these finite
temperature sum rules are discussed.
