What PhD field of study in physics is best for studying Lie Groups?

[Leo Authersh]

What field of study in physics (PhD) should I take if I want to study about Lie Groups?

 

[Vanadium 50]

You don't need a PhD in physics to learn about Lie Groups. You need to take a math class.

 

[Leo Authersh]

You don't need a PhD in physics to learn about Lie Groups. You need to take a math class.

No, I'm going to do PhD. And want to study advanced topics on Lie Groups. Just want to know which Field of Study in Physics do research on Lie Groups?

 

[fresh_42]

No, I'm going to do PhD. And want to study advanced topics on Lie Groups. Just want to know which Field of Study in Physics do research on Lie Groups?

None. Mathematicians do, but mainly on Lie groups which aren't of physical interest. QFT uses (some) Lie groups. Mathematically it's either a separate field or part of differential geometry and / or topology, sometimes analysis.

 

[George Jones]

No, I'm going to do PhD. And want to study advanced topics on Lie Groups. Just want to know which Field of Study in Physics do research on Lie Groups?

Did you mean: "which Field of Study in Physics uses advanced concepts of Lie Groups?"

 

[Leo Authersh]

Did you mean: "which Field of Study in Physics uses advanced concepts of Lie Groups?"

Yes.

 

[Leo Authersh]

None. Mathematicians do, but mainly on Lie groups which aren't of physical interest. QFT uses (some) Lie groups. Mathematically it's either a separate field or part of differential geometry and / or topology, sometimes analysis.

Because, the Physicists working on Unified Theory have remarked that the Group Theories are of great Significance to Unified Theory. So, I am looking for the possibility if some of the Physics' fields of study do research on Lie Groups.

 

[fresh_42]

Because, the Physicists working on Unified Theory have remarked that the Group Theories are of great Significance to Unified Theory. So, I am looking for the possibility if some of the Physics' fields of study do research on Lie Groups.

In physics, mainly semisimple Lie groups play a major role and these are already completely classified. Maybe the Poincaré and Heisenberg groups to some extend, too, but the crucial part are the simple groups in the standard model. Even the extensions of the theory concentrate on simple groups like $E_8$ or $SU(5)$. Things might change in the context of super string theory. Certainly super Lie algebras play a role here. I'm not so sure about the groups (if there are super versions at all).

 

[CrysPhys]

No, I'm going to do PhD. And want to study advanced topics on Lie Groups. Just want to know which Field of Study in Physics do research on Lie Groups?

Perhaps you should clarify your situation. Typically one gets interested in a particular field of physics and then learns the particular tools (math, software, experimental equipment, ...) needed to conduct research in it. You seem to be approaching it the other way around: You have a particular tool and want to know which field of physics uses it. So, are you a mathematician with expertise in Lie groups seeking to transition to a PhD in physics and wanting to leverage your existing expertise?

 

[Moayd Shagaf]

Usually Theoretical Particle Physics, And Quantum Field Theory, Will it's very important when you go in Gauge Theories like Electroweak And Quantum Chromodynamics, So If you are going to make research in The Physical Applications in Lie Groups then It well be probably in Particle Physics.