Light-cone operator expansions in perturbation theory. II

A systematic investigation, in perturbation theory, is presented of the light-cone behavior of multiparticle matrix elements of time-ordered products of local fields: $\int d^{4}x{e}^{idx}〈\beta \left|T{\psi }_1\right(x\left){\psi }_2\right(0\left)\right|\alpha 〉$. In the limit q₋→∞, the contribution of any single Feynman graph is of the form ${q_{-}}^{\beta }{\left(\ln q_{-}\right)}^{\gamma }$. The main result here is a rule by means of which the integers β and γ can be read off from the topology of the graph. The implications of this investigation for local field theories are organized and discussed in operator language in a companion paper. A by-product of the special methods here developed to obtain asymptotic estimates in perturbation theory is a refinement of Weinberg's theorem for the Euclidean region: the determination of the logarithmic factors in the asymptotic form of Feynman amplitudes when a set of external momenta q₁, q₂, ṡ is allowed to approach infinity according to qᵢ=ηq′ᵢ, η→∞.