# “Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model

## Abstract

The BPS Skyrme model is a model containing an SU(2)-valued scalar field, in which a Bogomol’nyi-type inequality can be satisfied by soliton solutions (skyrmions). In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-back of the Haar measure of the group SU(2) on the physical space by the field configuration. As a consequence, this energy expression has a high degree of symmetry: it is invariant to volume preserving diffeomorphisms both on physical space and on the target space. We demonstrate here that in the BPS Skyrme model such solutions exist that a fraction of its charge and energy densities is localised, and the remaining part can be far away, not interacting with the localised part.

- Authors:

- MTA Wigner RCP, RMI, P.O. Box 49, Budapest H1525 (Hungary)

- Publication Date:

- OSTI Identifier:
- 22596591

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 7; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MATHEMATICAL SOLUTIONS; SCALAR FIELDS; SOLITONS; SYMMETRY; TOPOLOGY

### Citation Formats

```
Lukács, Árpád.
```*“Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model*. United States: N. p., 2016.
Web. doi:10.1063/1.4959234.

```
Lukács, Árpád.
```*“Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model*. United States. doi:10.1063/1.4959234.

```
Lukács, Árpád. Fri .
"“Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model". United States.
doi:10.1063/1.4959234.
```

```
@article{osti_22596591,
```

title = {“Half a proton” in the Bogomol’nyi-Prasad-Sommerfield Skyrme model},

author = {Lukács, Árpád},

abstractNote = {The BPS Skyrme model is a model containing an SU(2)-valued scalar field, in which a Bogomol’nyi-type inequality can be satisfied by soliton solutions (skyrmions). In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-back of the Haar measure of the group SU(2) on the physical space by the field configuration. As a consequence, this energy expression has a high degree of symmetry: it is invariant to volume preserving diffeomorphisms both on physical space and on the target space. We demonstrate here that in the BPS Skyrme model such solutions exist that a fraction of its charge and energy densities is localised, and the remaining part can be far away, not interacting with the localised part.},

doi = {10.1063/1.4959234},

journal = {Journal of Mathematical Physics},

number = 7,

volume = 57,

place = {United States},

year = {Fri Jul 15 00:00:00 EDT 2016},

month = {Fri Jul 15 00:00:00 EDT 2016}

}