# Large N Expansion: Getting Started

• metamathphys
In summary, the conversation discusses the "large N expansion" method for SU(N) gauge theories and the difficulty in finding information about it in textbooks. Suggestions are made for resources, including Zee's "QFT in a Nutshell" and Manohar's notes on large N.
metamathphys
Hello.

Apparently for SU(N) gauge theories there is a perturvative approach call "large N expansion". I need a working knowledge of this method but I can not find it in any textbook only in research papers that are rather for the expert. Someone has any suggestion where should I get started?
Can it be found in Weinberg's?

Zee, QFT in a Nutshell, gives a short (3 pages) introduction to the idea.

I always liked some notes by Manohar http://arxiv.org/abs/hep-ph/9802419. The first several sections are generic, discussing both vector and matrix large N, while the later sections get into more detailed QCD physics.

Thank you very much. I already knew about Zee's but is too short I will give now a try to Manohar.

## 1. What is the Large N Expansion?

The Large N Expansion is a mathematical technique used to simplify calculations in quantum field theory. It involves taking the number of particles, or degrees of freedom, in a system to be very large, which allows for approximations to be made.

## 2. Why is the Large N Expansion useful?

The Large N Expansion allows for complicated calculations in quantum field theory to be simplified, making them easier to solve and providing valuable insights into the behavior of physical systems. It is commonly used in theoretical physics and has applications in various fields such as condensed matter physics and particle physics.

## 3. How is the Large N Expansion performed?

The Large N Expansion involves taking the number of particles or degrees of freedom in a system, denoted by N, to be very large. This allows for the use of mathematical techniques such as perturbation theory and saddle-point approximations, which are not possible for smaller N values.

## 4. What are the limitations of the Large N Expansion?

The Large N Expansion is a powerful tool, but it is not without its limitations. It is most useful for systems with a large number of particles or degrees of freedom, and may not be applicable to all physical systems. Additionally, the approximations made in the Large N Expansion may not always be accurate, and the results should be carefully interpreted.

## 5. Are there any practical applications of the Large N Expansion?

Yes, the Large N Expansion has numerous practical applications in physics research. It has been used to study phase transitions, quantum chromodynamics, and even the behavior of black holes. It also has applications in other fields such as statistics and computer science.

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