Other Electromagnetic Couplings
In this chapter we are concerned with other electrodynamic theories which show new features, not present in four-dimensional spinor QED. The new feature in scalar QED is the derivative coupling between the scalar field and the vector potential. It has important consequences for gauge invariance, in particular, the interaction gets modified by gauge invariance. Such derivative couplings also occur in Yang-Mills theories, and the same implications of gauge invariance appear here. This is briefly discussed in the Epilogue. The axial anomalies, that we describe next, provide an important example where gauge invariance partially breaks down. These anomalies also occur in the standard electro-weak theory and must be compensated there. This implies the lepton-quark duality, which means that to each lepton family (e, μ, τ) there must exist a corresponding quark family. Finally, if QED in two space plus one time dimensions is considered, the vacuum polarization shows unusual behaviour. This has the surprising consequence that the photon becomes massive. These examples illustrate how rich QED really is.
KeywordsGauge Invariance Tensor Structure Vacuum Polarization Normalization Term Electromagnetic Coupling
Unable to display preview. Download preview PDF.