Gauge Field Theories
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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.
KeywordsGauge Theory Higgs Boson Gauge Group Gauge Transformation Global Symmetry
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Suggestions for Further Reading
- Bailin, D. and Love, A., Introduction to Gauge Field Theory. Adam Hilger, Bristol 1986; Chaps. 9, 13Google Scholar
- Cheng, T.-P. and Li, L.-F., Gauge Theory of Elementary Particle Physics. Oxford U. Press, New York 1984Google Scholar
- Coleman, S., in Laws of Hadronic Matter. Academic Press, New York 1975Google Scholar
On gauge field theories
- Gell-Mann, M. and Glashow, S. L., Ann. Phys. (NY), 15 (1961) 437 Utiyama, R., Phys. Rev. 101 (1956) 1597Google Scholar
Lattice gauge theory
On Nambu-Goldstone’s theorem
The Higgs phenomenon
- Hooft, G., Nucl. Phys. B33 (1971) 173; B35 (1971) 167Google Scholar