Skeleton-graph approach to dynamical scaling

We use the skeleton-graph $\epsilon$-expansion method to discuss the critical dynamics of a Bose liquid in $d=4-\epsilon$ dimensions. The treatment is limited to the question of the behavior at the critical temperature of the frequency-dependent order-parameter correlation function (propagator) at zero momentum. We find that a power-law variation with frequency is only possible when the system acquires time-dependent Ginzburg-Landau behavior. Our analysis is incomplete in that the influence of collective modes on the critical behavior is not taken into account in detail. In an appendix, we present a powerful method for evaluating integrals associated with the Feynman graphs which arise in problems in critical phenomena.