Transport approach to multiparticle production: Collective phenomena and renormalization

We solve $\lambda {\phi }^4$ theory excited by a $c$- number source in the random-phase approximation as a prototypic model for investigating the relativistic transport approach to multiparticle production. We find that the pion field excited by the source exhibits collective behavior, with the collective mode first affecting the inclusive single-particle distribution at order $g^4$ in $E\frac{\mathrm{dN}}{d^{3}p}$ where $g$ is the coupling to the source. We give the renormalization prescription for the transport theory and derive the renormalized self-consistency equation for the theory with arbitrary source.