# Simple five-dimensional wave equation for a Dirac particle

## Abstract

A first-order relativistic wave equation is constructed in five dimensions. Its solutions are eight-component spinors, interpreted as single-particle fermion wave functions in four-dimensional space-time. Use of a ''cylinder condition'' (the removal of explicit dependence on the fifth coordinate) reduces each eight-component solution to a pair of degenerate four-component spinors. It is shown that, when the cylinder condition is applied, the results obtained from the new equation are the same as those obtained from the Dirac equation. Without the cylinder condition, on the other hand, the equation implies the existence of a scalar potential, and for zero-mass particles it leads to a four-dimensional fermionic equation analogous to Maxwell's equation with sources.

- Authors:

- Department of Physics, Texas Tech University, MS 1051, Lubbock, Texas 79409 (United States)

- Publication Date:

- OSTI Identifier:
- 20929635

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 2; Other Information: DOI: 10.1063/1.2435983; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COORDINATES; CYLINDERS; DIRAC EQUATION; FERMIONS; FOUR-DIMENSIONAL CALCULATIONS; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; MAXWELL EQUATIONS; POTENTIALS; QUANTUM MECHANICS; RELATIVISTIC RANGE; SCALARS; SPACE-TIME; SPINORS; WAVE FUNCTIONS

### Citation Formats

```
Redington, N., and Lodhi, M. A. K.
```*Simple five-dimensional wave equation for a Dirac particle*. United States: N. p., 2007.
Web. doi:10.1063/1.2435983.

```
Redington, N., & Lodhi, M. A. K.
```*Simple five-dimensional wave equation for a Dirac particle*. United States. doi:10.1063/1.2435983.

```
Redington, N., and Lodhi, M. A. K. Thu .
"Simple five-dimensional wave equation for a Dirac particle". United States.
doi:10.1063/1.2435983.
```

```
@article{osti_20929635,
```

title = {Simple five-dimensional wave equation for a Dirac particle},

author = {Redington, N. and Lodhi, M. A. K.},

abstractNote = {A first-order relativistic wave equation is constructed in five dimensions. Its solutions are eight-component spinors, interpreted as single-particle fermion wave functions in four-dimensional space-time. Use of a ''cylinder condition'' (the removal of explicit dependence on the fifth coordinate) reduces each eight-component solution to a pair of degenerate four-component spinors. It is shown that, when the cylinder condition is applied, the results obtained from the new equation are the same as those obtained from the Dirac equation. Without the cylinder condition, on the other hand, the equation implies the existence of a scalar potential, and for zero-mass particles it leads to a four-dimensional fermionic equation analogous to Maxwell's equation with sources.},

doi = {10.1063/1.2435983},

journal = {Journal of Mathematical Physics},

number = 2,

volume = 48,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}