Abstract
We show that it is possible to use the idea of group contraction together with the self-dual solutions for a Yang-Mills theory, to obtain the number of parameters which characterize such classical configurations. To be precise, quantum fluctuations about a Yang-Mills pseudo-particle solution are studied from the point of view of the spontaneous breakdown of conformal symmetry. It is argued that the linearization procedure by which one passes from the non-linear Yang-Mills equation to the linear equations for the small oscillation modes leads to a group contraction of the conformal group SO(5, 1) and it is this which allows the number of parameters of the classical self-dual (or anti-self-dual) solutions to be counted. This argument is applied to the gauge group SU( n), where n ⩾ 2.
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