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The Gauss Law: A Tale

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Classical and Quantum Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 229))

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Abstract

The Gauss law plays a basic role in gauge theories, enforcing gauge invariance and creating edge states and superselection sectors. This article surveys these aspects of the Gauss law in QED, QCD and nonlinear G/H models. It is argued that nonabelian superselection rules are spontaneously broken. That is the case with SU(3) of colour which is spontaneously broken to \(U(1)\times U(1)\). Nonlinear G/H models are reformulated as gauge theories and the existence of edge states and superselection sectors in these models is also established.

We dedicate this article to our friend Alberto Ibort on the occasion of his sixtieth birthday.

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Notes

  1. 1.

    In [20], Buchholz has proven that Lorentz transformations must be spontaneously broken in electrically charged sectors and also that electrically charged states cannot be eigenstates of the mass operators.

  2. 2.

    Fröhlich, Morchio and Strocchi base their work on the asymptotic fields (relying on Buchholz’s collision theory for massless Bosons [24]). In  [25], Buchholz relates the problem to the interacting (time zero) fields, i.e. Gauss law.

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Acknowledgements

The second author acknowledges financial support from the Faculty of Sciences of Universidad de los Andes through project INV-2017-51-1444.

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Authors and Affiliations

  1. Department of Physics, Syracuse University, Syracuse, NY, 13244-1130, USA

    A. P. Balachandran

  2. Departamento de Física, Universidad de los Andes, A.A. 4976-12340, Bogotá, Colombia

    A. F. Reyes-Lega

Authors
  1. A. P. Balachandran
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  2. A. F. Reyes-Lega
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Correspondence to A. P. Balachandran .

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Editors and Affiliations

  1. Università degli Studi di Napoli Federico II, Naples, Italy

    G. Marmo

  2. Institute of Mathematical Sciences (ICMAT), Madrid, Spain

    David Martín de Diego

  3. Universitat Politècnica de Catalunya, Barcelona, Spain

    Miguel Muñoz Lecanda

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Balachandran, A.P., Reyes-Lega, A.F. (2019). The Gauss Law: A Tale. In: Marmo, G., Martín de Diego, D., Muñoz Lecanda, M. (eds) Classical and Quantum Physics. Springer Proceedings in Physics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-030-24748-5_4

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