ABSTRACT
The current turns out that the four-Fermi theory cannot be renormalised. Its quantum corrections give rise to an infinite number of divergent terms that cannot be reabsorbed in a redefinition of a Lagrangian with a finite number of interactions. To enforce current conservation, we typically use gauge invariance. But gauge invariance would protect the vector particle from having a mass. The big puzzle was how to describe a massive vector particle that is nevertheless associated to the vector potential of a gauge field. The Landau–Ginzburg theory that gives an effective description of this phenomenon precisely coincides with scalar quantum electrodynamics. In a prosaic way one states that the massless excitation was ‘eaten’ by the longitudinal component of the photon, which in the process got a mass.
