The Lagrangian for the Standard Model

 The Standard Model (SM) is the theory that best explains and describes all the known fundamental particles of nature, and the forces of nature, minus gravity. It is the heart and soul of particle physics. It is built around quantum field theory, which is, as one might expect, is one of the more challenging mathematical theories around. 

The main way to represent all the possible interactions and forces between the different particles is through a Lagrangian operator. Lagrangians are actually a standard way to do classical mechanics, and it can be extended into quantum mechanics, as well. A lagrangian is put together using energy, rather than forces like we would do in Newtonian mechanics. Think of a lagrangian as U - KE, or potential energy - kinetic energy. 

Anyhow, this article allows you to see what the lagrangian in the SM looks like, and breaks it down section by section to show you what the real math looks like for different interactions that build up our fundamental understanding of the universe!!