# Non-Abelian Yang-Mills analogue of classical electromagnetic duality

## Abstract

The classic question of non-Abelian Yang-Mills analogue to electromagnetic duality is examined here in a minimalist fashion at the strictly four-dimensional, classical field, and point charge level. A generalization of the Abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the Abelian theory. For example, there is a dual potential, but it is a two-indexed tensor {ital T}{sub {mu}{nu}} of the Freedman-Townsend-type. Though not itself functioning as such, {ital T}{sub {mu}{nu}} gives rise to a dual parallel transport {ital {tilde A}}{sub {mu}} for the phase of the wave function of the color magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard color (electric) charge itself is found to be a monpole of {ital {tilde A}}{sub {mu}}. At the same time, the gauge symmetry is found doubled from say SU({ital N}) to SU({ital N}){times}SU({ital N}). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a ``universal`` principle, namely, the Wu-Yang criterion for monpoles, where interactions arise purely as a consequence of the topological definition of themore »

- Authors:

- Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX (United Kingdom)
- Department of Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP (United Kingdom)
- Mathematical Institute, Oxford University, 24-29 St. Giles`, Oxford, OX1 3LB (United Kingdom)

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 135446

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review, D; Journal Volume: 52; Journal Issue: 10; Other Information: PBD: 15 Nov 1995

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; YANG-MILLS THEORY; DUALITY; ELECTROMAGNETISM; POTENTIALS; TENSORS; MONOPOLES; GAUGE INVARIANCE; EQUATIONS OF MOTION

### Citation Formats

```
Chan, Hong-Mo, Faridani, J., and Tsun, T.S..
```*Non-Abelian Yang-Mills analogue of classical electromagnetic duality*. United States: N. p., 1995.
Web. doi:10.1103/PhysRevD.52.6134.

```
Chan, Hong-Mo, Faridani, J., & Tsun, T.S..
```*Non-Abelian Yang-Mills analogue of classical electromagnetic duality*. United States. doi:10.1103/PhysRevD.52.6134.

```
Chan, Hong-Mo, Faridani, J., and Tsun, T.S.. Wed .
"Non-Abelian Yang-Mills analogue of classical electromagnetic duality". United States. doi:10.1103/PhysRevD.52.6134.
```

```
@article{osti_135446,
```

title = {Non-Abelian Yang-Mills analogue of classical electromagnetic duality},

author = {Chan, Hong-Mo and Faridani, J. and Tsun, T.S.},

abstractNote = {The classic question of non-Abelian Yang-Mills analogue to electromagnetic duality is examined here in a minimalist fashion at the strictly four-dimensional, classical field, and point charge level. A generalization of the Abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the Abelian theory. For example, there is a dual potential, but it is a two-indexed tensor {ital T}{sub {mu}{nu}} of the Freedman-Townsend-type. Though not itself functioning as such, {ital T}{sub {mu}{nu}} gives rise to a dual parallel transport {ital {tilde A}}{sub {mu}} for the phase of the wave function of the color magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard color (electric) charge itself is found to be a monpole of {ital {tilde A}}{sub {mu}}. At the same time, the gauge symmetry is found doubled from say SU({ital N}) to SU({ital N}){times}SU({ital N}). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a ``universal`` principle, namely, the Wu-Yang criterion for monpoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov.},

doi = {10.1103/PhysRevD.52.6134},

journal = {Physical Review, D},

number = 10,

volume = 52,

place = {United States},

year = {Wed Nov 15 00:00:00 EST 1995},

month = {Wed Nov 15 00:00:00 EST 1995}

}