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arXiv · hep-th/9403031

The Wu-Yang Ambiguity Revisited

Daniel Z. Freedman·Ramzi R. Khuri
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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 $B\neq 0$). 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 $Γ_{jk}^i$ with torsion defined from gauge covariant derivatives of $B$.

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Daniel Z. Freedman, Ramzi R. Khuri. 1994-03-04. The Wu-Yang Ambiguity Revisited. https://doi.org/10.1016/0370-2693(94)90770-6

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