Spectral function sum rules from current algebra, unitarity and analyticity

With the assumptions of SU(2)*SU(2) current algebra, conservation of the vector currents, PCAC and finiteness of the Schwinger terms C/sub V/ and C/sub A/, some restrictions of unitarity and analyticity on hard pion current algebra models are obtained for the specific case of the pion form factor. Among the results are a representation for the proper vertex of the vector current between pion states, the Kawarabayashi-Suzuki-Fayyazuddin-Riazuddin relation and other spectral function sum rules. In the case of polynomial models for the proper vertices, a lower bound on C/sub V/ and an upper bound for the rho width are derived, and estimates are made of corrections to rho pole dominance of the vector current spectral function. (17 refs).