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The Nielsen identities for the two-point functions of QED and QCD

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Zeitschrift für Physik C Particles and Fields

Abstract

We consider the Nielsen identities for the twopoint functions of full QCD and QED in the class of Lorentz gauges. For pedagogical reasons the identities are first derived in QED to demonstrate the gauge independence of the photon self-energy, and of the electron mass shell. In QCD we derive the general identity and hence the identities for the quark, gluon and ghost propagators. The explicit contributions to the gluon and ghost identities are calculated to one-loop order, and then we show that the quark identity requires that in on-shell schemes the quark mass renormalisation must be gauge independent. Furthermore, we obtain formal solutions for the gluon selfenergy and ghost propagator in terms of the gauge dependence of other, independent Green functions.

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Authors and Affiliations

  1. Department of Physics and Engineering Physics and Saskatchewan Accelerator Lab, University of Saskatchewan, S7N 0W0, Saskatoon, Saskatchewan, Canada

    J. C. Breckenridge & T. G. Steele

  2. Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, Postfach 3980, D-55099, Mainz, Germany

    M. J. Lavelle

Authors
  1. J. C. Breckenridge
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  2. M. J. Lavelle
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  3. T. G. Steele
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Breckenridge, J.C., Lavelle, M.J. & Steele, T.G. The Nielsen identities for the two-point functions of QED and QCD. Z. Phys. C - Particles and Fields 65, 155–164 (1995). https://doi.org/10.1007/BF01571316

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  • DOI: https://doi.org/10.1007/BF01571316

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