The Wu-Yang Ambiguity Revisited

Abstract

Several examples are given of continuous families of SU(2) vector potentials $A_i^a(x)$ in 3 space dimensions which generate the same magnetic field $B^{ai}(x)$ (with det $B\ne 0$). These Wu-Yang families are obtained from the Einstein equation $R_{ij}=-2G_{ij}$ derived recently via a local map of the gauge field system into a spatial geometry with $2$-tensor $G_{ij}=B^a{}_i{B}^a{}_j\det B$ and connection ${\Gamma }_{jk}^i$ with torsion defined from gauge covariant derivatives of $B$.

12 pages, CERN-TH.7187/94, CTP#2282 (previous version missing acknowledgements)

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• Extremal Curves in 2+1-Dimensional Yang-Mills Theory
• Spatial Geometry of Non-Abelian Gauge Theory in \(2 + 1\) Dimensions
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• Concerning gauge field fluctuations around classical configurations
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