Dirac and Seiberg-Witten monopoles. (English) Zbl 0985.53019

Naber, Gregory L.

Mladenov, I. M. (ed.) et al., Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, September 1-10, 1999. Sofia: Coral Press Scientific Publishing. 181-199 (2000).

In his proceedings contribution the author gives an informal survey of the relation between Seiberg-Witten monopoles and its non-Abelian generalization on Minkowski space-time. The author starts with a brief summary on Dirac monopoles considered as natural connections on non-trivial principal U(1)-bundles over \(S^2\) (Hopf-bundles). He then discusses Dirac monopoles as solutions to the SU(2) Yang-Mills-Higgs equations on \(\mathbb{R}^3\) as well as to the field equations of the Seiberg-Witten theory. The author finally discusses the Dirac monopole as a solution of the SU(2) generalization to the Seiberg-Witten field equations on Minkowski space-time \(R^{1,3}\). The presentation of the paper is very explicit and clear.
For the entire collection see [Zbl 0940.00039].

Reviewer: Jürgen Tolksdorf (Mannheim)

MSC:

53C07	Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
57R57	Applications of global analysis to structures on manifolds
53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
81T13	Yang-Mills and other gauge theories in quantum field theory
58E15	Variational problems concerning extremal problems in several variables; Yang-Mills functionals

Keywords:

Minkowski space-time; Yang-Mills-Higgs equations; Dirac monopole