Theories and Lagrangians II: Introducing Gauge Fields
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.
KeywordsGauge Theory Gauge Group Gauge Transformation Gauge Invariance Gauge Field
- 8.Dirac, P.A.M.: Lectures on Quantum Mechanics, Dover, NY (2001)Google Scholar
- 9.Henneaux, M., Teitelboim, C.: Quantization of Gauge Systems, Princeton Press, Princeton,(1992)Google Scholar
- 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
- 16.Rubakov, V.: Theory of Gauge Fields, Princeton Press, Princeton (1999)Google Scholar