Abstract
Models of hadrons that are rooted in light-front (LF) formulation of QCD have been linked to the classical field equations in a 5-dimensional anti-de Sitter (AdS) gravitational background in terms of the Brodsky-de Téramond LF holography. We discuss the classical equations of motion for the expectation values of operators in quantum field theory whose nature resembles the Ehrenfest equations of quantum mechanics and which thus appear to provide a general justification for the holographic picture. The required expectation values are obtained by distinguishing one effective constituent of a hadron, the one that is struck by an external electro-weak or gravitational probe, and integrating over relative motion variables of all other constituents in all Fock components. The scale-dependent Fock decomposition of hadronic states is defined using the renormalization group procedure for effective particles. The AdS modes dual to the incoming and outgoing hadrons in the corresponding transition matrix elements are thus found equivalent to the Gaussian form distribution functions for the effective partons struck by external probes.
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