Exploring the Applications of Galois Theory in Physics

[kostas230]

I don't know if this is the correct section to post this, but does Galois theory has any applications in physics?

 

[homeomorphic]

Google it and stuff will come up.

I don't know if it has SERIOUS applications. You can google almost any math topic AND physics and you'll often find something. However, it's always hard to know if the applications are really meaningful.

I'll take the opportunity to point out, though, that the point of math is often indirect. Galois and Lagrange and those guys invented group theory in the context of solving polynomial equations. And groups play a big role in physics. So, I don't know about Galois theory, but spin-offs of Galois theory do have a role to play. That's often the way it works. I'm guessing 90% of pure math isn't directly useful, I think, but a bigger percentage is indirectly useful.

 

[Jim Kata]

I'll give you two examples. If you think about the fundamental group as a galois group then yes. You know from topology that the fundamental group as it acts on deck transformations is analogous to how the Galois group acts on field extensions. What is the fundamental group (Galois group) of the Lorentz group? It's Z/2Z this is why there are only fermions and bosons. In 2D surface physics the fundamental group is Z this is why there can be anyons in 2D physics. Another more math based example comes from the Langlands correspondence in physics, namely the fundamental group of the adjoint representation is isomorphic to the center of a simply connected dual group.