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Spatial Geometry and the Wu-Yang Ambiguity

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 sys...

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Detalles Bibliográficos
Autores principales: Freedman, Daniel Z., Khuri, Ramzi R.
Lenguaje:eng
Publicado: 1994
Materias:
Acceso en línea:https://dx.doi.org/10.1007/3-540-59163-X_274
http://cds.cern.ch/record/467451
Descripción
Sumario: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 $B$.