# The application of light-cone quantization to quantum chromodynamics in one-plus-one dimensions

## Abstract

Formal and computational aspects of light cone quantization are studied by application to quantum chromodynamics (QCD) in one spatial plus one temporal dimension. This quantization scheme, which has been extensively applied to perturbative calculations, is shown to provide an intuitively appealing and numerically tractable approach to non-perturbative computations as well. In the initial section, a light-cone quantization procedure is developed which incorporates fields on the boundaries. This allows for the consistent treatment of massless fermions and the construction of explicitly conserved momentum and charge operators. The next section, which comprises the majority of this work, focuses on the numerical solution of the light-cone Schrodinger equation for bound states. The state space is constructed and the Hamiltonian is evaluated and diagonalized by computer for arbitrary number of colors, baryon number and coupling constant strength. As a result, the full spectrum of mesons and baryons and their associated wavefunctions are determined. These results are compared with those which exist from other approaches to test the reliability of the method. The program also provides a preliminary test for the feasibility of, and an opportunity to develop approximation schemes for, an attack on three-plus-one dimensional QCD. Finally, analytic results are presented which include amore »

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center, Menlo Park, CA (USA)

- OSTI Identifier:
- 6783753

- Report Number(s):
- SLAC-333

ON: DE89006019

- DOE Contract Number:
- AC03-76SF00515

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM CHROMODYNAMICS; QUANTIZATION; HAMILTONIANS; INTEGRAL EQUATIONS; LIGHT CONE; MATRIX ELEMENTS; PERTURBATION THEORY; QUARKS; SCHROEDINGER EQUATION; STRUCTURE FUNCTIONS; USES; WAVE FUNCTIONS; DIFFERENTIAL EQUATIONS; ELEMENTARY PARTICLES; EQUATIONS; FIELD THEORIES; FUNCTIONS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; POSTULATED PARTICLES; QUANTUM FIELD THEORY; QUANTUM OPERATORS; SPACE-TIME; WAVE EQUATIONS; 645400* - High Energy Physics- Field Theory

### Citation Formats

```
Hornbostel, K J.
```*The application of light-cone quantization to quantum chromodynamics in one-plus-one dimensions*. United States: N. p., 1988.
Web. doi:10.2172/6783753.

```
Hornbostel, K J.
```*The application of light-cone quantization to quantum chromodynamics in one-plus-one dimensions*. United States. doi:10.2172/6783753.

```
Hornbostel, K J. Thu .
"The application of light-cone quantization to quantum chromodynamics in one-plus-one dimensions". United States. doi:10.2172/6783753. https://www.osti.gov/servlets/purl/6783753.
```

```
@article{osti_6783753,
```

title = {The application of light-cone quantization to quantum chromodynamics in one-plus-one dimensions},

author = {Hornbostel, K J},

abstractNote = {Formal and computational aspects of light cone quantization are studied by application to quantum chromodynamics (QCD) in one spatial plus one temporal dimension. This quantization scheme, which has been extensively applied to perturbative calculations, is shown to provide an intuitively appealing and numerically tractable approach to non-perturbative computations as well. In the initial section, a light-cone quantization procedure is developed which incorporates fields on the boundaries. This allows for the consistent treatment of massless fermions and the construction of explicitly conserved momentum and charge operators. The next section, which comprises the majority of this work, focuses on the numerical solution of the light-cone Schrodinger equation for bound states. The state space is constructed and the Hamiltonian is evaluated and diagonalized by computer for arbitrary number of colors, baryon number and coupling constant strength. As a result, the full spectrum of mesons and baryons and their associated wavefunctions are determined. These results are compared with those which exist from other approaches to test the reliability of the method. The program also provides a preliminary test for the feasibility of, and an opportunity to develop approximation schemes for, an attack on three-plus-one dimensional QCD. Finally, analytic results are presented which include a discussion of integral equations for wavefunctions and their endpoint behavior. Solutions for hadronic masses and wavefunctions in the limits of both large and small quark mass are discussed. 49 refs., 32 figs., 10 tabs.},

doi = {10.2172/6783753},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1988},

month = {12}

}