Yang-Mills self-dual solutions and the conformal group contraction

P. Tataru-Mihai and G. Vitiello

Physica A: Statistical Mechanics and its Applications, 1982, vol. 114, issue 1, 229-232

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.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:114:y:1982:i:1:p:229-232

DOI: 10.1016/0378-4371(82)90288-6

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