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

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Discussion Overview

The discussion centers around the appropriate field of study within physics for pursuing advanced research on Lie Groups, particularly in the context of a PhD program. Participants explore the relevance of Lie Groups in various physics domains, including theoretical frameworks and applications.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants suggest that a PhD in physics is not necessary to study Lie Groups, proposing that relevant mathematical coursework suffices.
  • Others emphasize that Lie Groups are primarily studied by mathematicians, with limited direct physical applications, although Quantum Field Theory (QFT) utilizes some Lie Groups.
  • A participant notes that semisimple Lie groups are significant in physics, particularly in the context of the standard model and unified theories, mentioning specific groups like ##E_8## and ##SU(5)##.
  • There is a suggestion that the participant should clarify their background and intentions, as they seem to be approaching the topic from a mathematical perspective rather than a physics-focused one.
  • One participant indicates that Theoretical Particle Physics and Quantum Field Theory are relevant fields for research involving Lie Groups, particularly in gauge theories.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of a PhD in physics for studying Lie Groups, with some asserting that it is not required while others focus on the importance of specific physics fields that utilize these mathematical structures. The discussion remains unresolved regarding the best path for studying Lie Groups within physics.

Contextual Notes

Participants highlight the distinction between the mathematical study of Lie Groups and their application in physics, indicating that the relevance of certain groups may depend on the specific area of research within physics.

Leo Authersh
What field of study in physics (PhD) should I take if I want to study about Lie Groups?
 
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You don't need a PhD in physics to learn about Lie Groups. You need to take a math class.
 
Vanadium 50 said:
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?
 
Leo Authersh said:
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.
 
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Leo Authersh said:
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?"
 
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George Jones said:
Did you mean: "which Field of Study in Physics uses advanced concepts of Lie Groups?"
Yes.
 
fresh_42 said:
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.
 
Leo Authersh said:
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).
 
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Leo Authersh said:
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?
 
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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.
 
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