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Covariant Hamiltonian Representation of Noether’s Theorem and Its Application to SU(N) Gauge Theories

  • Jürgen StruckmeierEmail author
  • Horst Stöcker
  • David Vasak
Chapter
Part of the FIAS Interdisciplinary Science Series book series (FIAS)

Abstract

We present the derivation of the Yang-Mills gauge theory based on the covariant Hamiltonian representation of Noether’s theorem. As the starting point, we re-formulate our previous presentation of the canonical Hamiltonian derivation of Noether’s theorem (Struckmeier and Reichau, Exciting Interdisciplinary Physics, Springer, New York, p. 367, 2013, [1]). The formalism is then applied to derive the Yang-Mills gauge theory. The Noether currents of U(1) and SU(N) gauge theories are derived from the respective infinitesimal generating functions of the pertinent symmetry transformations which maintain the form of the respective Hamiltonian.

Notes

Acknowledgments

This paper is prepared for the Symposium on Exciting Physics, which was held in November 2015 at Makutsi Safari Farm, South Africa, to honor our teacher, mentor, and friend Prof. Dr. Dr. h.c. mult. Walter Greiner on the occasion of his 80th birthday. We thank Walter for stimulating generations of young scientists for more than 100 semesters, both at the Goethe Universität Frankfurt am Main and internationally. We wish him good health to further take part in the progress of physics in the years to come. We furthermore thank the present members of our FIAS working group on the Extended canonical formalism of field theory, namely Michail Chabanov, Matthias Hanauske, Johannes Kirsch, Adrian Koenigstein, and Johannes Muench for many fruitful discussions.

References

  1. 1.
    J. Struckmeier, H. Reichau, General U(N) gauge Transformations in the Realm of Covariant Hamiltonian Field Theory, in: Exciting Interdisciplinary Physics. FIAS Interdisciplinary Science Series (Springer, New York, 2013), P. 367. http://arxiv.org/abs/1205.5754
  2. 2.
    E. Noether, Nachr. Königl. Ges. Wiss. Göttingen, Math.-Phys. Kl. 57, 235 (1918)Google Scholar
  3. 3.
    J.V. José, E.J. Saletan, Classical Dynamics (Cambridge University Press, Cambridge, 1998)CrossRefzbMATHGoogle Scholar
  4. 4.
    J. Struckmeier, A. Redelbach, Int. J. Mod. Phys. E 17, 435 (2008). http://arxiv.org/abs/0811.0508
  5. 5.
    W. Greiner, Classical Electrodynamics (Springer, 1998)Google Scholar
  6. 6.
    T. De Donder, Théorie Invariantive Du Calcul des Variations (Gaulthier-Villars & Cie, Paris, 1930)zbMATHGoogle Scholar
  7. 7.
    H. Weyl, Ann. Math. 36, 607 (1935)MathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Koenigstein, J. Kirsch, H. Stoecker, J. Struckmeier, D. Vasak, M. Hanauske, Int. J. Mod. Phys. E 25, 1642005 (2016). doi: 10.1142/S0218301316420052 ADSCrossRefGoogle Scholar
  9. 9.
    J. Struckmeier, D. Vasak, H. Stoecker, A. Koenigstein, J. Kirsch, M. Hanauske, J. A. Muench, in preparation (2016)Google Scholar
  10. 10.
    D. Vasak, J. Struckmeier, H. Stoecker, A. Koenigstein, J. Kirsch, M. Hanauske, in preparation (2016)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Jürgen Struckmeier
    • 1
    • 2
    Email author
  • Horst Stöcker
    • 1
    • 2
    • 3
    • 4
  • David Vasak
    • 3
  1. 1.GSI Helmholtzzentrum Für Schwerionenforschung GmbHDarmstadtGermany
  2. 2.Goethe UniversitätFrankfurt am MainGermany
  3. 3.Frankfurt Institute for Advanced Studies (FIAS)FrankfurtGermany
  4. 4.Institute of Theoretical Physics (ITP), Goethe UniversityFrankfurt am MainGermany

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