Really quick explanation for gauge theory?

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Discussion Overview

The discussion centers around the concept of gauge theory, specifically seeking a quick explanation and clarification of related topics such as SU symmetry breaking. Participants express varying levels of familiarity with the subject and share resources for further reading.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Meta-discussion

Main Points Raised

  • One participant requests a concise explanation of gauge theory, indicating a lack of understanding of related concepts like SU symmetry breaking.
  • Another participant suggests that providing a "quick explanation" is challenging due to the complexity and depth of gauge theory, sharing several links to resources that may help.
  • A participant defines gauge theory as involving "unphysical" variables where different values correspond to the same physical situation, using the electric potential as an example.
  • They mention Yang-Mills quantum field theory as a notable example of a gauge theory, discussing the use of both physical and unphysical variables in different contexts.
  • Some participants express uncertainty about the backgrounds of forum members, with one noting that not everyone is a university professor and sharing their own self-taught experience in quantum mechanics and relativity.
  • Another participant echoes the sentiment that gauge theory is elegant yet difficult to grasp at a lay level, suggesting that understanding some technicalities of quantum mechanics may aid comprehension.

Areas of Agreement / Disagreement

Participants generally agree that gauge theory is complex and challenging to explain succinctly. However, there is no consensus on a simplified explanation or a shared understanding of the topic among all participants.

Contextual Notes

Participants express varying levels of familiarity with gauge theory, and there are references to different educational backgrounds, indicating a mix of expertise and self-taught knowledge. The discussion includes links to external resources that may not be universally accessible or comprehensible.

Who May Find This Useful

This discussion may be useful for individuals seeking an introductory understanding of gauge theory, those interested in the backgrounds of other forum members, and learners looking for resources to further their knowledge in quantum mechanics and related fields.

CookieSalesman
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Could anyone give a really quick explanation for gauge theory to me?
Or a link, or a book is perfectly fine.
I just completely don't understand SU symmetry breaking and etc. etc.

I also have a question, is everyone who lurks around here a college professor on quantum physics or something? It seems that everyone knows a lot around here.

Sorry for double thread, I'll ask for this to be del'd after a few responses.
 
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CookieSalesman said:
Could anyone give a really quick explanation for gauge theory to me?

It's nigh impossible to give a "quick explanation" of something so elegant and deep. Here are some readings that don't use too much technical language:

http://scistud.umkc.edu/psa98/papers/weinstein.pdf
http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Quigley.pdf
http://www.ippp.dur.ac.uk/~krauss/Lectures/IntoToParticlePhysics/2010/Lecture9.pdf
http://www.iop.vast.ac.vn/theor/conferences/vsop/18/files/QFT-4.pdf

CookieSalesman said:
I also have a question, is everyone who lurks around here a college professor on quantum physics or something?

No.
 
Last edited by a moderator:
:OSo what are you guys?
Not high school students or undergrads, right?
 
CookieSalesman said:
Not high school students or undergrads, right?

I'm sure there are some, who knows. Suffice it to say, not everyone here is a university professor :smile:
 
A gauge theory is a theory in which one uses variables that are "unphysical", ie. different values of the variable correspond to the same physical situation. A gauge transformation is a "do nothing" transformation, since although it changes the values of the variables, the physical situation remains unchanged. A very simple example of a gauge variable is the electric potential: one can add any constant to the potential without changing the physical situation, since it is only the potential difference which is physical.

A famous gauge theory is Yang-Mills quantum field theory. There the physical variables are loops. In some cases, the physical variables are used (eg. lattice gauge theory), while in other cases unphysical gauge variables are used because they are calculationally convenient (eg. the path integral presentation found in most textbooks).

(I'm a biologist.)
 
WannabeNewton said:
It's nigh impossible to give a "quick explanation" of something so elegant and deep.

Very true. Its has breathtaking elegance and beauty. It is very deep. But at the lay level, unfortunately, quite opaque.

But if you understand some of the technicalities of QM the following I posted before may be of value:
http://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html

Thanks
Bill
 
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CookieSalesman said:
I also have a question, is everyone who lurks around here a college professor on quantum physics or something? It seems that everyone knows a lot around here.

There are many like that - but certainly not all.

I suspect I am in the minority, but not alone, in not being formally trained in physics

I have a degree in applied math but self taught myself QM and relativity.

The good news for those that aren't a 'college professor on quantum physics or something' is learning this stuff can be done. The bad news is it took me a while.

Thanks
Bill
 
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