# Classification of gauge fields

## Abstract

It is shown that the Lorentz invariants of an arbitrary gauge field are double valued functions of a Lorentz invariant matrix L/sup i/j when rank L=3 and single valued functions of L/sup i/j when rank Lnot =3. The question of how many Lorentz inequivalent realizations of the Lorentz invariants there are is answered. This leads naturally to a classification of an arbitrary gauge field at a space--time point, given previously by Anandan and Tod based on the rank of L. The answer to the analogous question for the gauge invariants of the SU(2) gauge field leads to a new classification of this field. Five more classifications of this field, including one which is symmetric with respect to space--time and isospin groups, are also presented.

- Authors:

- Publication Date:

- Research Org.:
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

- OSTI Identifier:
- 6584571

- Alternate Identifier(s):
- OSTI ID: 6584571

- Resource Type:
- Journal Article

- Journal Name:
- J. Math. Phys. (N.Y.); (United States)

- Additional Journal Information:
- Journal Volume: 20:2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM FIELD THEORY; GAUGE INVARIANCE; ISOSPIN; LORENTZ INVARIANCE; SPACE-TIME; SU-2 GROUPS; FIELD THEORIES; INVARIANCE PRINCIPLES; LIE GROUPS; PARTICLE PROPERTIES; SU GROUPS; SYMMETRY GROUPS 645400* -- High Energy Physics-- Field Theory

### Citation Formats

```
Anandan, J.
```*Classification of gauge fields*. United States: N. p., 1979.
Web. doi:10.1063/1.524075.

```
Anandan, J.
```*Classification of gauge fields*. United States. doi:10.1063/1.524075.

```
Anandan, J. Thu .
"Classification of gauge fields". United States. doi:10.1063/1.524075.
```

```
@article{osti_6584571,
```

title = {Classification of gauge fields},

author = {Anandan, J.},

abstractNote = {It is shown that the Lorentz invariants of an arbitrary gauge field are double valued functions of a Lorentz invariant matrix L/sup i/j when rank L=3 and single valued functions of L/sup i/j when rank Lnot =3. The question of how many Lorentz inequivalent realizations of the Lorentz invariants there are is answered. This leads naturally to a classification of an arbitrary gauge field at a space--time point, given previously by Anandan and Tod based on the rank of L. The answer to the analogous question for the gauge invariants of the SU(2) gauge field leads to a new classification of this field. Five more classifications of this field, including one which is symmetric with respect to space--time and isospin groups, are also presented.},

doi = {10.1063/1.524075},

journal = {J. Math. Phys. (N.Y.); (United States)},

number = ,

volume = 20:2,

place = {United States},

year = {1979},

month = {2}

}