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The transformations of non-abelian gauge fields under translations

High Energy Physics - Theory 2007-05-23 v3

Abstract

I consider infinitesimal translations xα=xα+δxαx'^{\alpha}=x^{\alpha}+\delta x^{\alpha} and demand that Noether's approach gives a symmetric energy-momentum tensor as it is required for gravitational sources. This argument determines the transformations of non-abelian gauge fields under infinitesimal translations to differ from the usually assumed invariance by the gauge transformation, Aγa(x)Aγa(x)=γ[δxβAaβ(x)]+CbcaδxβAcβ(x)Aγb(x)A'^a_{\gamma} (x') - A^a_{\gamma}(x) = \partial_{\gamma} [ \delta x_{\beta} A^{a \beta}(x)] + C^a_{bc} \delta x_{\beta} A^{c \beta}(x) A^{b}_{\gamma}(x) where the CbcaC^a_{bc} are the structure constants of the gauge group.

Keywords

Cite

@article{arxiv.hep-th/0006045,
  title  = {The transformations of non-abelian gauge fields under translations},
  author = {Bernd A. Berg},
  journal= {arXiv preprint arXiv:hep-th/0006045},
  year   = {2007}
}

Comments

References to work by Jackiw and others are added