Mathematical formulation of the Standard Model

Summary

The Standard Model of particle physics is a gauge theory on Minkowski space with gauge group $SU(3) \times SU(2) \times U(1)$. Its mathematical formulation lists the representations in which the matter fields transform and the Lagrangian density that couples them. It combines quantum chromodynamics with the electroweak theory, in which the Higgs mechanism breaks $SU(2) \times U(1)$ down to the $U(1)$ of electromagnetism. It describes all known elementary particles and every known force except gravity.