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Monopole BPS-Solutions of the Yang-Mills Equations in Space of Euclid, Riemann, and Lobachevski

V. M. Red'kov
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Abstract

Procedure of finding of the Bogomolny-Prasad-Sommerfield monopole solutions in the Georgi-Glashow model is investigated in detail on the backgrounds of three space models of constant curvature: Euclid, Riemann, Lobachevski's. Classification of possible solutions is given. It is shown that among all solutions there exist just three ones which reasonably and in a one-to-one correspondence can be associated with respective geometries. It is pointed out that the known non-singular BPS-solution in the flat Minkowski space can be understood as a result of somewhat artificial combining the Minkowski space background with a possibility naturally linked up with the Lobachewski geometry. The standpoint is brought forth that of primary interest should be regarded only three specifically distinctive solutions -- one for every curved space background. In the framework of those arguments the generally accepted status of the known monopole BPS-solution should be critically reconsidered and even might be given away.

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V. M. Red'kov. 2003-06-07. Monopole BPS-Solutions of the Yang-Mills Equations in Space of Euclid, Riemann, and Lobachevski. https://arxiv.org/abs/hep-th/0306060

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