From condensed matter to QCD: a journey through gauge theories on board of a variational tool

Starting with a review of the thermal fluctuations in superconductors, the Gaussian Effective Potential is shown to be a powerful variational tool for the study of the breaking of symmetry in gauge theories. A novel re-derivation of the massive expansion for QCD is presented, showing its variational nature and its origin from the Gaussian potential that also provides a variational proof for chiral symmetry breaking and dynamical generation of a gluon mass.