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.
Highlights
Perturbative QCD successfully describes high-energy collisions of hadrons using parton models [1], but encounters difficulties with explaining physics of hadrons understood as bound states of quarks [2,3] as far as observables that are not accessible using Euclidean lattice formulation of QCD [4] are concerned
The Maldacena conjecture of anti-de Sitter (AdS)/CFT duality [5] has been used by Polchinsky and Strassler [6,7] to argue that hadrons may be described in terms of classical fields in a five-dimensional space-time, hopefully providing a initial approximation to the physics of hadrons. de Téramond and Brodsky [8,9] discovered that the Polchinski and Strassler formulae for form factors of mesons are precisely matched by the corresponding formulae in the light-front (LF) formulation of quantum field theory (QFT) when one identifies the differential equation in 5th dimension for a meson field with the transverse radial eigenvalue equation for a meson valence wave function in the LF Fock space
In this paper we discuss an example which shows that the Ehrenfest correspondence principle between quantum and classical mechanics [10] can be adapted to provide, in combination with the LF holography, a natural explanation of how a complex QFT could reduce to the simple dual picture [11]
Summary
Perturbative QCD successfully describes high-energy collisions of hadrons using parton models [1], but encounters difficulties with explaining physics of hadrons understood as bound states of quarks [2,3] as far as observables that are not accessible using Euclidean lattice formulation of QCD [4] are concerned. De Téramond and Brodsky [8,9] discovered that the Polchinski and Strassler formulae for form factors of mesons are precisely matched by the corresponding formulae in the light-front (LF) formulation of quantum field theory (QFT) when one identifies the differential equation in 5th dimension for a meson field with the transverse radial eigenvalue equation for a meson valence wave function in the LF Fock space. We assume that the front form (FF) of Hamiltonian dynamics [12] yields a representation of eigenstates that correspond to hadrons in terms of a suitably defined effective Fock-space expansion once the theory is renormalized using the renormalization group procedure for effective particles (RGPEP) [13]. Where the eigenvalue is expressed using the kinematical components P+ and P⊥ of the total momentum of the system and its mass squared, M2
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