A Rigorous Spectral Representation of Relativistic Random Phase Approximation

A rigorous spectral representation of relativistic random-phase approximation is presented. Explicit expression is derived for the effective particle-hole interaction which contains the direct term K_an, the exchange term K_sc and the kernel for the fermion line renormalization K_fr. It is shown that according to our method, not only K_anan but also K_sc and K_fr can be given rigorously in a form which depends only on one ω(energy)-variable and they all take account of the retardation effect properly.