Conservation laws, symmetries, and in particular gauge symmetries are fundamental to the construction of the standard model of particle physics. And as we've seen in past videos, the link that connects symmetries and conservation laws is Noether's theorem.

In this video, we'll see how it all extends to field theories. We'll learn to formulate a local conservation law by writing down its continuity equation, which describes how charge is conserved in any region of space. Then we'll see how these conservation laws appear any time we have a field theory with a continuous symmetry.

We'll learn about the symmetry of electromagnetism, called U(1), that leads to the conservation of electric charge. And finally, we'll see how to write down the simplest example of a gauge theory by coupling to the electromagnetic potential. The global U(1) symmetry becomes a local symmetry thanks to the covariant derivative, and we arrive at a U(1) gauge theory! The standard model is a generalization of all this.

↩ Back to all videos