ABSTRACT
The framework of field theory allows the definition of a class of transformations other than spacetime transformations. These are the internal transformations which, due to Noether's theorem, also lead to conserved currents and charges. We first discuss global phase transformations and subsequently the more general local phase transformations of fields, also called gauge transformations. Gauge symmetry provides a powerful guiding principle in order to define the interaction between different types of fields. The gauge symmetry leads to a coupling prescription that fully determines the interaction between fields. The Maxwell electromagnetic field interacting with a matter field represents the prime example. In this chapter, we discuss the resulting Lagrangian densities, the equations of motion, and the associated conserved currents and energy-momentum tensors.
