Yang Mills & Fiber Bundles Resource

In summary, the conversation is about finding a resource for learning Yang-Mills theory and Fiber Bundles that is intuitive and provides a geometric understanding of gauge theory. The participants discuss a few book recommendations, but none of them seem to be exactly what the person is looking for. They also mention the book "Nakahara's Geometry, Topology & Physics" and "Fecko's Differential Geometry and Lie Groups for Physicists" as potential options. The conversation ends with a recommendation for a book that covers the mathematical foundations of QFT and is written in a more formal style.
  • #1
quickAndLucky
34
3
Hi everyone,
Does anyone know of a good intuitive resource for learning Yang-Mills theory and Fiber Bundles? Ultimately my goal is to gain a geometric understanding of gauge theory generally. I have been studying differential forms and exterior calculus. Thanks!
 
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  • #2
I know several resources for this topic, but I don't find any of them particularly intuitive. So I will wait to see what will the others recommend.
 
  • #3
Demystifier said:
I know several resources for this topic, but I don't find any of them particularly intuitive. So I will wait to see what will the others recommend.
Nobody else seems to have anything in mind. Would appreciate hearing what you have used!
 
  • #4
quickAndLucky said:
Nobody else seems to have anything in mind. Would appreciate hearing what you have used!
I'm interested in the answers, as well, especially because of the intuition requirement. My own intuition ends with the imagination of a field of wheat. And from there to the technical details is a long, long way.
 
  • #6
Nakahara’s Geometry, Topology & Physics is a popular choice. I started learning differential geometry from it.
 
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  • #8
I'ver recently found

https://www.amazon.com/dp/3319684388/?tag=pfamazon01-20

I've not read much in the book yet. So I can't say, whether it's good or not, but it seems to cover a lot of the mathematical foundations, usually not found in standard QFT textbooks for physicists, and it's written in the Mathematicians' dry style ;-)).
 
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FAQ: Yang Mills & Fiber Bundles Resource

1. What is Yang Mills theory?

Yang Mills theory is a mathematical framework used to describe the interactions between elementary particles in the field of quantum physics. It is based on the concept of gauge symmetry and has been successful in predicting the behavior of fundamental particles.

2. What is the role of fiber bundles in Yang Mills theory?

Fiber bundles are mathematical objects used to describe the local structure of gauge fields in Yang Mills theory. They help to understand the geometric properties of these fields and their transformation under gauge transformations.

3. How is Yang Mills theory related to the Standard Model of particle physics?

Yang Mills theory is a fundamental part of the Standard Model of particle physics. It provides the mathematical framework for describing the strong and weak nuclear forces, which are two of the four fundamental forces in the Standard Model.

4. What is the significance of Yang Mills theory in modern physics?

Yang Mills theory has been a major breakthrough in the field of theoretical physics. It has successfully predicted the existence and properties of fundamental particles, and has been tested and confirmed by numerous experiments. It also plays a crucial role in the development of other theories, such as superstring theory and quantum field theory.

5. Are there any current research developments in Yang Mills theory?

Yes, there is ongoing research in Yang Mills theory, particularly in its application to other areas of physics such as cosmology and condensed matter physics. One current focus is on understanding the role of topology in Yang Mills theory, which could lead to new insights and applications.

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