Quantum Effective Actions in Weyl-flat Spacetimes and Applications

Computing quantum effective actions is paramount to any semi-classical problem in quantum field theory. However the calculation can be extremely challenging in the presence of complicated sources or of a curved spacetime. It is possible to progress when the sources and the gravitational field are weak, however some very relevant physical situations require strong fields and are beyond any such approximations. Half of this thesis is devoted to developing a technique capable of computing effective actions reliably, without assuming a weak gravitational field. The results are applicable to classically Weyl-invariant theories living in Weyl-flat spacetimes. The second half of the thesis is devoted to an application of this particular method. Relatively intense magnetic fields exist in the universe, coherent at Mpc scales. Such fields call for a primordial origin, however to date there is no clear understanding on how they are created. The hypothesis that they are of quantum origin, coming from the Weyl anomaly of the Standard Model itself has been discussed in the past, with some results claiming positively that this is indeed possible. We use our methods developed in the first half of the thesis to settle the issue proving it is actually impossible to generate such fields from the Weyl anomaly of the standard model alone. We conclude that such fields, if they exist, must originate from something beyond the Standard Model.