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:
Particle Physics - Theory
Acceso en línea:https://dx.doi.org/10.1007/3-540-59163-X_274
http://cds.cern.ch/record/467451
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author Freedman, Daniel Z.
Khuri, Ramzi R.
author_facet Freedman, Daniel Z.
Khuri, Ramzi R.
author_sort Freedman, Daniel Z.
collection CERN
description 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 $B$.
id cern-467451
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1994
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spelling cern-4674512023-03-14T20:43:28Zdoi:10.1007/3-540-59163-X_274http://cds.cern.ch/record/467451engFreedman, Daniel Z.Khuri, Ramzi R.Spatial Geometry and the Wu-Yang AmbiguityParticle Physics - TheoryWe 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 $B$.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 $B$.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 $B$.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 $B$.hep-th/9412151CERN-TH-7466-94CERN-TH.7466-94MCGILL-94-52CERN-TH-7466-94MCGILL-94-52oai:cds.cern.ch:4674511994
spellingShingle Particle Physics - Theory
Freedman, Daniel Z.
Khuri, Ramzi R.
Spatial Geometry and the Wu-Yang Ambiguity
title Spatial Geometry and the Wu-Yang Ambiguity
title_full Spatial Geometry and the Wu-Yang Ambiguity
title_fullStr Spatial Geometry and the Wu-Yang Ambiguity
title_full_unstemmed Spatial Geometry and the Wu-Yang Ambiguity
title_short Spatial Geometry and the Wu-Yang Ambiguity
title_sort spatial geometry and the wu-yang ambiguity
topic Particle Physics - Theory
url https://dx.doi.org/10.1007/3-540-59163-X_274
http://cds.cern.ch/record/467451
work_keys_str_mv AT freedmandanielz spatialgeometryandthewuyangambiguity
AT khuriramzir spatialgeometryandthewuyangambiguity

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