Abstract
These three lectures will be complementary to the earlier lectures on solitons in that they will deal with solitons in physical, three-dimensional space. On the other hand, the solitons will be purely classical. The relevance of of gauge-theory to solitons solutions is that, according to an argument of Derrick(1), static solitons (finite energy solutions of the field equations) can be constructed from scalar fields alone in only one space dimension, and a natural possibility to overcome this problem is to use vector, or gauge fields. Recently it has been shown that static solitons in two, three and even four dimensions, can indeed be constructed in this way. We shall be interested principly in the static solitons in three dimensions, whose existence was first noted (2) by ’t Hooft and Polyakov. In the first lecture the ’t H-P soliton, together with two simple generalizations of it, will be presented. In the following two lectures we shall be concerned with further generalizations of this soliton, particularly generalizations with higher values of the magnetic charge.
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O’Raifeartaigh, L. (1978). Classical Static Gauge-Field Solitons in Three Space Dimensions. In: Streit, L. (eds) Many Degrees of Freedom in Field Theory. NATO Advanced Study Institutes Series, vol 30. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8924-2_4
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DOI: https://doi.org/10.1007/978-1-4615-8924-2_4
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