Central limit theorem in quantum field theory, generalized partons and application to deep-inelastic scattering

Abstract

We prove the following elementary theorem. Ifφ1,...,φN is a sequence of fields having identical, thougharbitrary, interactions but not interacting with each other and 〈φn〉0,i=1,...,N then the generating functional of the «average» field φ(N) may be explicitly obtained and may be written in terms of the two-point function of any of the fields φi. The theorem is then applied to define generalized parton fields\(\psi _j = \sum\limits_{i = 1}^N {\psi _{ij} } /\sqrt N \) as «averages» of basic fieldsψij havingarbitrary interactions but not interacting with each other. We show that in the limitN→∞ Bjorken scaling, as observed at energies not too high, may be obtained if only quanta associated with generalized parton fields are excited in the hadron by the virtual photonwith no reference to the details of the underlying dynamics. ForN<∞, and the excitation of other quanta as well lead to a systematic breaking of scale invariance and the details of the dynamics are necessarily recovered which are expected to be applicable at higher energy regimes.