# Light-Front Holography and the Light-Front Schrodinger Equation

## Abstract

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 wellmore »

- Authors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1049748

- Report Number(s):
- SLAC-PUB-15211

arXiv:1208.3020; TRN: US1204476

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Conference

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

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; AMPLITUDES; APPROXIMATIONS; BOUND STATE; CEBAF ACCELERATOR; DIMENSIONS; EIGENVALUES; EXCITATION; FORM FACTORS; GLUONS; HADRONS; HAMILTONIANS; HOLOGRAPHY; NUCLEONS; PIONS; QUANTIZATION; QUANTUM CHROMODYNAMICS; QUARKS; SPECTRA; SPECTROSCOPY; VALENCE; Phenomenology-HEP, Theory-HEP,HEPPH, HEPTH

### Citation Formats

```
Brodsky, Stanley J, and de Teramond, Guy.
```*Light-Front Holography and the Light-Front Schrodinger Equation*. United States: N. p., 2012.
Web.

```
Brodsky, Stanley J, & de Teramond, Guy.
```*Light-Front Holography and the Light-Front Schrodinger Equation*. United States.

```
Brodsky, Stanley J, and de Teramond, Guy. Wed .
"Light-Front Holography and the Light-Front Schrodinger Equation". United States. https://www.osti.gov/servlets/purl/1049748.
```

```
@article{osti_1049748,
```

title = {Light-Front Holography and the Light-Front Schrodinger Equation},

author = {Brodsky, Stanley J and de Teramond, Guy},

abstractNote = {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.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {8}

}