Framework for generating multi-monopole solutions

Technical Report · Thu Jan 01 04:00:00 EST 1981

OSTI ID:6440251

Chau Wang, L L

The 't Hooft-Polyakov monopole solution is discussed and it is shown that in the limit of vanishing Higgs potential the monopole solution corresponds to the self-dual Yang-Mills solution depending only on three of the four coordinates. The formulation of self-dual Yang-Mills equations in complex 4-Euclidean space, the R-gauge and the BI transformation are presented. In this formulation every BI-transformation increases the monopole charge by one unit, if the resulting solution can be shown to have non-singular energy density and real potential. The conditions for non-singularity and reality are explicitly given. The explicit one and two monopole solutions are discussed in this formalism. The multi-monopole solutions of Prasad and Rossi are given, with comment on the use of the BI transformation to generate solutions to the Ernst equation, which miraculously is identical to self-dual Yang-Mills equation in the R-gauge for geometry with axial symmetry.

• Research Organization: Brookhaven National Lab., Upton, NY (USA)
• DOE Contract Number: AC02-76CH00016
• OSTI ID: 6440251
• Report Number(s): BNL-29550; ON: DE81025072
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANALYTICAL SOLUTION
ELEMENTARY PARTICLES
FOUR-DIMENSIONAL CALCULATIONS
HIGGS MODEL
LIE GROUPS
MAGNETIC MONOPOLES
MATHEMATICAL MODELS
MONOPOLES
PARTICLE MODELS
POSTULATED PARTICLES
SU GROUPS
SU-2 GROUPS
SYMMETRY
SYMMETRY GROUPS
YANG-MILLS THEORY