Spatial Geometry and the Wu-Yang Ambiguity

Details Spatial Geometry and the Wu-Yang Ambiguity Spatial Geometry and the Wu-Yang Ambiguity

1994-12-16

arxiv.org/abs/hep-th/9412151v2

Physics

High Energy Physics

High Energy Physics - Theory

Based on talks given by R. Khuri at PASCOS-94, Syracuse University, May 1994 and at Gursey Memorial Conference I, Istanbul, Ju

Scientific paper

We display 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 $\Gamma_{jk}^i$ with torsion defined from gauge covariant derivatives of $B$.

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