Uniqueness of Pseudoparticle Potential of the Form f(x)g<-1>∂_μg with O(3) Symmetric Unitary g

概要

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The pseudoparticle solutions in Euclidean SU(2) Yang-Mills theory are searched among the potentials of the form A_μ=f(x)g^<-1>∂_μg, where g is restricted to O(3) symmetric unitary matrix. Concerning the coefficient function f(x), nothing is presupposed. The conclusion is that the only potentials of this form giving the self-dual or anti-self-dual field are those obtained by Belavin et al. [the BPST potentials], which represent single-pseudo-particle (instanton or anti-instanton) configurations. Also the inverse-radius transforms of the BPST potentials are shown to be additional solutions, provided that a certain prescription is adopted for handling the singularities of potentials. However, under the same prescription, the transformations connecting these additional solutions with the original BPST potentials are shown just to be non-singular gauge transformations.
一般社団法人日本物理学会の論文
1978-12-25