Double dispersion relations in quantum Statistical Mechanics—II

Abstract

Double dispersion relations are given for the functions $$\gamma (12;3) = \frac{1}{i}\langle T\left( {\psi (1)\psi ^\dag (2)B (3)} \right)\rangle$$ common in many electron problems. Here ψ and ψT refer to electron destruction and creation operators, and B (3) is a boson or boson-like operator such as particle density, ion displacement, local spin, particle current density, or electron spin density. Consequences of Hermiticity properties and time reversal invariance as well as sum rules are established for the spectral density functions entering the double dispersion relations. A subtracted double dispersion relation is suggested for the corresponding vertex function. Details of the derivation and examples are given which were not included in an earlier brief report of this work.