Light-Cone Operator Expansions in Perturbation Theory. I

Abstract

With the aid of a general algorithm for expanding a given Heisenberg operator product in terms of $n$-particle irreducible operator products integrated over $c$-number Bethe-Salpeter kernels, we discuss the expansion of bilocal products near the light cone. It is shown that, to any finite order in perturbation theory, only a small number of terms in the operator-product expansion can be singular on the light cone. In particular, some of the bilocal operators which determine the scaling properties of deep-inelastic electroproduction have potential singularities determined by operator-valued Bethe-Salpeter equations involving only these bilocals themselves (plus local fields). A generalization of the light-cone Bjorken-Johnson-Low (BJL) limit is given which reveals logarithmic singularities which occur in $T$ products but not in commutators; this BJL limit is applied systematically to Feynman graphs in another paper. As a special case, the Wilson expansion is recovered.

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