Advertisement

Gauge Field Theories

Chapter
  • 308 Downloads

Abstract

All the current successful theories of the fundamental forces start from the premise of invariance of the physical laws to certain coordinate-dependent transformations. In particular, the quantum field theories of the electromagnetic, weak, and strong interactions of the fundamental particles all belong to the class of local gauge theories, so called because they are invariant to coordinate-dependent transformations on internal space of the particles. We start this chapter by describing the general relation between symmetries and interactions. Next, we take up the study of invariance under the Abelian gauge group U(l), the group of space-time-dependent phase transformations on charged fields; the resulting gauge theory is electrodynamics. The following section is devoted to theories for which the gauge group is non-Abelian. The results see immediate applications to quantum chromodynamics, a theory based on the color SU(3) group. The last two sections of the chapter contain a discussion on the mechanism of spontaneous symmetry breaking, which is an indispensable ingredient in the formulation of the standard theory of the electroweak interaction, the subject of the following chapter.

Keywords

Gauge Theory Higgs Boson Gauge Group Gauge Transformation Global Symmetry 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Suggestions for Further Reading

General references

  1. Abers, E. S. and Lee, B. W., Phys. Rep 9C (1973) 1ADSCrossRefGoogle Scholar
  2. Aitchison, I. J. R. and Hey, A. J. G., Gauge Theories in Particle Physics ( Second edition ). Adam Hilger, Bristol 1989; Chap. 9zbMATHCrossRefGoogle Scholar
  3. Bailin, D. and Love, A., Introduction to Gauge Field Theory. Adam Hilger, Bristol 1986; Chaps. 9, 13Google Scholar
  4. Cheng, T.-P. and Li, L.-F., Gauge Theory of Elementary Particle Physics. Oxford U. Press, New York 1984Google Scholar
  5. Coleman, S., in Laws of Hadronic Matter. Academic Press, New York 1975Google Scholar

On gauge field theories

  1. Gell-Mann, M. and Glashow, S. L., Ann. Phys. (NY), 15 (1961) 437 Utiyama, R., Phys. Rev. 101 (1956) 1597Google Scholar
  2. Yang, C. N. and Mills, R. L., Phys. Rev. 96 (1954) 191MathSciNetADSCrossRefGoogle Scholar

Quantum electrodynamics

  1. Kinoshita, T., Quantum Electrodynamics. World Scientific, Singapore 1990zbMATHGoogle Scholar
  2. Schweber, S. S., QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga. Princeton U. Press, Princeton 1994Google Scholar
  3. Schwinger, Julian Selected Papers on Quantum Electrodynamics. Dover, New York 1958Google Scholar

Quantum chromodynamics

  1. Fritzsch, H., Gell-Mann, M. and Leutwyler, H., Phys. Lett. 47B (1973) 365Google Scholar
  2. Gross, D. J. and Wilczek, F., Phys. Rev. D8 (1973) 3633ADSGoogle Scholar
  3. Marciano, W. and Pagels, H., Phys. Rep. 36C (1978) 137ADSCrossRefGoogle Scholar
  4. Politzer, H. D., Phys. Rep. 14C (1974) 129ADSCrossRefGoogle Scholar
  5. Weinberg, S., Phys. Rev. Lett. 31 (1973) 494ADSCrossRefGoogle Scholar
  6. Wilczek, F., Ann. Rev. Nucl. and Part. Sci. 32 (1982) 177ADSCrossRefGoogle Scholar
  7. Yndurâin, F. J., Quantum Chromodynamics, An Introduction to the Theory of Quarks and Flavors. Springer, Berlin, Heidelberg 1983Google Scholar

Lattice gauge theory

  1. Creutz, M., Quarks, Gluons, and Lattices. Cambridge U. Press, Cambridge 1983Google Scholar
  2. Lattice 96, Nucl. Phys. (Proc. Suppl.) B53 (1997) February 1997Google Scholar
  3. Rebbi, C., Lattice Gauge Theories and Monte Carlo Simulations. World Scientific, Singapore 1983Google Scholar
  4. Wilson, K. G., Phys. Rev. D10 (1974) 2445; Rev. Mod. Phys. 47 (1975) 773ADSCrossRefGoogle Scholar

On Nambu-Goldstone’s theorem

  1. Nambu, Y., Phys. Rev. Lett. 4 (1960) 380ADSCrossRefGoogle Scholar
  2. Goldstone, J., Nuovo Cimento 19 (1961) 154MathSciNetzbMATHCrossRefGoogle Scholar
  3. Goldstone, J., Salam, A. and Weinberg, S., Phys. Rev. 127 (1962) 965MathSciNetADSzbMATHCrossRefGoogle Scholar

The Higgs phenomenon

  1. Englert, F. and Brout, R., Phys. Rev. Lett. 13 (1964) 321MathSciNetADSCrossRefGoogle Scholar
  2. Guralnik, G., Hagen, C. and Kibble, T., Phys. Rev. Lett. 13 (1964) 585ADSCrossRefGoogle Scholar
  3. Higgs, P., Phys. Lett. 12 (1964) 132; Phys. Rev. 145 (1966) 1156Google Scholar
  4. Kibble, T., Phys. Rev. 155 (1967) 1554Google Scholar

Renormalization

  1. Hooft, G., Nucl. Phys. B33 (1971) 173; B35 (1971) 167Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  1. 1.Physics DepartmentUniversité LavalSte-FoyCanada
  2. 2.Laboratoire de Physique Théorique et Hautes EnergiesUniversités Paris VI et VIIParis Cedex 05France

Personalised recommendations