The known Euclidean Yang-Mills pseudoparticle solutions with Pontryagin index n are parametrized by $5n$ constants describing the size and location of each pseudoparticle. By insisting on conformal covariance of the solutions, we show that more general solutions exist---they are parametrized by $5n+4$ constants. We further demonstrate that the additional degrees of freedom are not gauge artifacts and correspond to a new degeneracy of pseudoparticle configurations.
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Jackiw et al. (1977) studied this question.
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