Light-Front Holography and the Light-Front Schrodinger Equation

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One of the most important nonperturbative methods for solving QCD is quantization at fixed light-front time {tau} = t+z=c - Dirac's 'Front Form'. The eigenvalues of the light-front QCD Hamiltonian predict the hadron spectrum and the eigensolutions provide the light-front wavefunctions which describe hadron structure. More generally, we show that the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrodinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. We outline a method for computing the required potential ... continued below

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Brodsky, Stanley J. & de Teramond, Guy August 15, 2012.

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One of the most important nonperturbative methods for solving QCD is quantization at fixed light-front time {tau} = t+z=c - Dirac's 'Front Form'. The eigenvalues of the light-front QCD Hamiltonian predict the hadron spectrum and the eigensolutions provide the light-front wavefunctions which describe hadron structure. More generally, we show that the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrodinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. We outline a method for computing the required potential from first principles in QCD. The holographic mapping of gravity in AdS space to QCD, quantized at fixed light-front time, yields the same light front Schrodinger equation; in fact, the soft-wall AdS/QCD approach provides a model for the light-front potential which is color-confining and reproduces well the light-hadron spectrum. One also derives via light-front holography a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent first approximation of the color-confining dynamics, spectroscopy, and excitation spectra of relativistic light-quark bound states in QCD.

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  • Invited talk at QCD Evolution Workshop, 14-17 May 2012: Newport News, Virginia, USA

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  • Report No.: SLAC-PUB-15211
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 1049748
  • Archival Resource Key: ark:/67531/metadc828629

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • August 15, 2012

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  • May 19, 2016, 9:45 a.m.

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  • June 20, 2016, 7:17 p.m.

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Brodsky, Stanley J. & de Teramond, Guy. Light-Front Holography and the Light-Front Schrodinger Equation, article, August 15, 2012; United States. (digital.library.unt.edu/ark:/67531/metadc828629/: accessed December 16, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.