### Abstract

An Abelian gauge field theory framed on a complex line bundle L over a compact Riemann surface M is developed which allows the coexistence, simultaneously in the same model, of magnetic vortices and antivortices represented by the N zeros and P poles of a section of L. The quantized minimum energy E is given in terms of the first Chern class ci(L) and by a certain intersection number obtained from the multivortices. We show that E = 2ir(N + P). To realize such topological invariants as minimum energies, an existence and uniqueness theorem is established under the necessary and sufficient condition that |ci(L)| = \N -P\ < (total volume of M)/27r.

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

Pages (from-to) | 593-613 |

Number of pages | 21 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 456 |

Issue number | 1995 |

State | Published - 2000 |

### Fingerprint

### Keywords

- Characteristic classes
- Complex line bundles
- Leray-schauder theorem
- Self-duality
- Trudinger-moser inequality
- Vortices

### ASJC Scopus subject areas

- General

### Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*456*(1995), 593-613.

**Abelian gauge theory on Riemann surfaces and new topological invariants.** / Sibner, Lesley; Sibner, Robert; Yang, Yisong.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 456, no. 1995, pp. 593-613.

}

TY - JOUR

T1 - Abelian gauge theory on Riemann surfaces and new topological invariants

AU - Sibner, Lesley

AU - Sibner, Robert

AU - Yang, Yisong

PY - 2000

Y1 - 2000

N2 - An Abelian gauge field theory framed on a complex line bundle L over a compact Riemann surface M is developed which allows the coexistence, simultaneously in the same model, of magnetic vortices and antivortices represented by the N zeros and P poles of a section of L. The quantized minimum energy E is given in terms of the first Chern class ci(L) and by a certain intersection number obtained from the multivortices. We show that E = 2ir(N + P). To realize such topological invariants as minimum energies, an existence and uniqueness theorem is established under the necessary and sufficient condition that |ci(L)| = \N -P\ < (total volume of M)/27r.

AB - An Abelian gauge field theory framed on a complex line bundle L over a compact Riemann surface M is developed which allows the coexistence, simultaneously in the same model, of magnetic vortices and antivortices represented by the N zeros and P poles of a section of L. The quantized minimum energy E is given in terms of the first Chern class ci(L) and by a certain intersection number obtained from the multivortices. We show that E = 2ir(N + P). To realize such topological invariants as minimum energies, an existence and uniqueness theorem is established under the necessary and sufficient condition that |ci(L)| = \N -P\ < (total volume of M)/27r.

KW - Characteristic classes

KW - Complex line bundles

KW - Leray-schauder theorem

KW - Self-duality

KW - Trudinger-moser inequality

KW - Vortices

UR - http://www.scopus.com/inward/record.url?scp=0042725110&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042725110&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0042725110

VL - 456

SP - 593

EP - 613

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 1995

ER -