Theories and Lagrangians II: Introducing Gauge Fields

Part of the Lecture Notes in Physics book series (LNP, volume 839)


Gauge theories play a central role in our current understanding of the fundamental interactions. The weak, electromagnetic and strong interactions are well described by gauge theories. We introduce them in this chapter for the first time. Although we often talk about gauge invariance, or gauge symmetry, these terms are a bit misleading. The gauge symmetry is more a redundancy in the description of the physical degrees of freedom than a symmetry, as will be shown later on. The redundancy is of course very useful because it makes Lorentz invariance and locality explicit, but it is not a symmetry in the same sense as rotations or translations. These theories have an incredible richness and complexity. Many aspects of their dynamics are still poorly understood. In our presentation we just scratch the surface of a deep subject.


Gauge Theory Gauge Group Gauge Transformation Gauge Invariance Gauge Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Aharonov, Y., Bohm, D.: Significance of the electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485 (1955)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Ehrenberg, W., Siday, R.E.: The refractive index in electron optics and the principles of dynamics. Proc. Phys. Soc. B 62, 8 (1949)ADSCrossRefGoogle Scholar
  3. 3.
    Dirac, P.A.M.: Quantised singularities in the electromagnetic field. Proc. Roy. Soc. 133, 60 (1931)ADSCrossRefGoogle Scholar
  4. 4.
    Schwinger, J.: Sources and magnetic charge. Phys. Rev. 173, 1544 (1968)ADSCrossRefGoogle Scholar
  5. 5.
    Zwanziger, D.: Exactly soluble nonrelativistic model of particles with both electric and magnetic charges. Phys. Rev. 176, 1480 (1968)ADSCrossRefGoogle Scholar
  6. 6.
    ’t Hooft, G.: Magnetic monopoles in unified gauge theories. Nucl. Phys. B 79, 276 (1974)MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Polyakov, A.M.: Particle spectrum in the quantum field theory. JETP Lett 20, 194 (1974)ADSGoogle Scholar
  8. 8.
    Dirac, P.A.M.: Lectures on Quantum Mechanics, Dover, NY (2001)Google Scholar
  9. 9.
    Henneaux, M., Teitelboim, C.: Quantization of Gauge Systems, Princeton Press, Princeton,(1992)Google Scholar
  10. 10.
    Jackiw, R.: Quantum meaning of classical field theory. Rev. Mod. Phys. 49, 681 (1977)MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    Jackiw, R.: Introduction to the Yang–Mills quantum theory. Rev. Mod. Phys. 52, 661 (1980)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Jackiw, R.: Topological investigations of quantized gauge theories. In: DeWitt, B.S., Stora, R. (eds) Relativité, groupes et topologie II. Elsevier, London (1984)Google Scholar
  13. 13.
    Faddeev, L.D., Popov, V.N.: Feynman diagrams for the Yang–Mills field. Phys. Lett. B 25, 29 (1967)ADSCrossRefGoogle Scholar
  14. 14.
    Nakahara, M.: Geometry, topology and physics. Institute of Physics, UK (1990)zbMATHCrossRefGoogle Scholar
  15. 15.
    ‘t Hooft, G.: The topological mechanism for permanent quark confinement in a Nonabelian gauge theory. Phys. Scripta 25, 133 (1982)ADSCrossRefGoogle Scholar
  16. 16.
    Rubakov, V.: Theory of Gauge Fields, Princeton Press, Princeton (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Theory Unit, Physics DepartmentCERNGenevaSwitzerland
  2. 2.Departamento de Física FundamentalUniversidad de SalamancaSalamancaSpain

Personalised recommendations