Abstract
Gauge field configuration for a magnetic monopole and its dual configuration are studied in SU(2) gauge theory. We present a relation between the monopole field and its dual field. Since these fields can become massive, their massive Lagrangians are derived. In the dual case, an additional term appears. We show this term is necessary to produce a linear potential between a monopole charge and an antimonopole charge.
Highlights
Magnetic monopoles are considered to play an important role in quark confinement
By modifying Eq(B2), we find Eq(B9) is satisfied by the solution z−r rρ[2] e−mr
Iv we can apply the usual Wick rotation, which is performed by the replacement p0 → −ip[4] and dp0 → i dp[4]
Summary
Magnetic monopoles are considered to play an important role in quark confinement. Models based on the dual superconductor require monopoles and their condensation (see, e.g., [1]). We study the relation between the Abelian magnetic potential and its dual potential. Based on this relation, we consider the confinement of magnetic charges. By using the dual magnetic potential, we rewrite the Abelian part of the SU(2) Lagrangian with the monopole field. Massless magnetic potential is considered, and massive magnetic potential is studied in Sect. 6, using the Lagrangian, it is shown that the static potential between a magnetic monopole and an anti-monopole is a linear confining potential. For both the massless case and the massive case, the monopole solutions and their dual solutions for a static magnetic charge are given in Appendix B.
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