On the structure of the Yang-Mills-Higgs equations on R³
The Yang-Mills-Higgs theory has its origins in Physics. It describes particles with masses via the Higgs mechanism and predicts magnetic monopoles. We study here the mathematical aspects of the theory following an analytical and geometric approach. Our motivation comes from physics and we work all the time with the full Lagrangian of the theory. At the same time, we are interested in it from the variational point of view, as a functional on an infinite dimensional space and as a system of non-linear equations on a non-compact manifold with finite energy as the only constraint. We are concerned mainly with the configuration space of the theory, the existence of solutions and their behaviour at infinity.