### Abstract

We prove the existence and uniqueness of a spherically symmetric monopole solution in the Abelian model of Lee and Weinberg in the BPS limit. The solution carries finite energy and unit charge and generalizes the classical SU(2) BPS monopole. We also prove an existence theorem for the model with a general Higgs field-dependent mass term and establish the equivalence of the second-order equations of motion and the first-order Bogomol'nyi equations within radial symmetry assumption and BPS limit. Our methods have wide applicability in other monopole problems.

Original language | English (US) |
---|---|

Pages (from-to) | 215-240 |

Number of pages | 26 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 117 |

Issue number | 1-4 |

State | Published - 1998 |

### Fingerprint

### Keywords

- Calculus of variations
- Gauge theory
- Minimization
- Monopoles

### ASJC Scopus subject areas

- Applied Mathematics
- Statistical and Nonlinear Physics

### Cite this

*Physica D: Nonlinear Phenomena*,

*117*(1-4), 215-240.

**The Lee-Weinberg magnetic monopole of unit charge : Existence and uniqueness.** / Yang, Yisong.

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 117, no. 1-4, pp. 215-240.

}

TY - JOUR

T1 - The Lee-Weinberg magnetic monopole of unit charge

T2 - Existence and uniqueness

AU - Yang, Yisong

PY - 1998

Y1 - 1998

N2 - We prove the existence and uniqueness of a spherically symmetric monopole solution in the Abelian model of Lee and Weinberg in the BPS limit. The solution carries finite energy and unit charge and generalizes the classical SU(2) BPS monopole. We also prove an existence theorem for the model with a general Higgs field-dependent mass term and establish the equivalence of the second-order equations of motion and the first-order Bogomol'nyi equations within radial symmetry assumption and BPS limit. Our methods have wide applicability in other monopole problems.

AB - We prove the existence and uniqueness of a spherically symmetric monopole solution in the Abelian model of Lee and Weinberg in the BPS limit. The solution carries finite energy and unit charge and generalizes the classical SU(2) BPS monopole. We also prove an existence theorem for the model with a general Higgs field-dependent mass term and establish the equivalence of the second-order equations of motion and the first-order Bogomol'nyi equations within radial symmetry assumption and BPS limit. Our methods have wide applicability in other monopole problems.

KW - Calculus of variations

KW - Gauge theory

KW - Minimization

KW - Monopoles

UR - http://www.scopus.com/inward/record.url?scp=22244483462&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22244483462&partnerID=8YFLogxK

M3 - Article

VL - 117

SP - 215

EP - 240

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-4

ER -