What is the ladder approximation and how does it work?

In summary, the conversation is about the ladder approximation in statistical field theory and condensed matter. The ladder approximation corresponds to the summation of a certain class of Feynman diagrams, but the person asking has been unable to find much information on it. They are looking for a book that explains how it works, in which cases it can be used, and what it neglects. Another person suggests looking at R. Mattuck's book, which covers the ladder approximation in chapter 10.
  • #1
ledamage
36
0
Hi there!

In some papers related to statistical field theory and condensed matter I've encountered the ladder approximation. It apparently corresponds to the summation of a certain class of Feynman diagrams. I've tried Google and some field theory books to learn more about this but I've found nothing, at least nothing pedagogigal.

Does anyone know a book which explains the ladder approximation? I want to know how it exactly works, in which cases it can be used and what the approximation actually neglects.

Thanks!
ledamage
 
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  • #2
The book of Gross (relativistic quantum mechanics and field theory) covers it I think
 
  • #3
I think you should take a look at R. Mattuck, "A Guide to Feynman Diagrams in the Many-Body Problem", chap. 10 (Dyson's equation, Renormalization, RPA and Ladder Approximations). You can find the book in Google Books.
 

Related to What is the ladder approximation and how does it work?

What is ladder approximation?

Ladder approximation is a mathematical technique used to estimate the behavior of a system with an infinite number of possible states. It is often used in quantum field theory and statistical mechanics, where the number of particles or energy levels in a system is too large to calculate exactly.

How does ladder approximation work?

In ladder approximation, the system is simplified by considering only a finite number of states, typically those with the highest energy. The interactions between these states are then approximated using simplified mathematical models, such as perturbation theory or mean-field theory.

When is ladder approximation used?

Ladder approximation is used when the system being studied is too complex to analyze using exact methods. It is also used when the interactions between the states are weak, making the simplified models accurate enough to provide useful insights into the behavior of the system.

What are the limitations of ladder approximation?

Ladder approximation is an approximation method and is not exact. It can lead to inaccuracies in the predicted behavior of the system, especially when the interactions between states are strong. It also does not take into account the effects of quantum fluctuations, which can be important in some systems.

What are some real-world applications of ladder approximation?

Ladder approximation has been used to study a wide range of physical systems, including superconductors, magnets, and polymers. It has also been applied in condensed matter physics, nuclear physics, and astrophysics to study the properties of matter at the atomic and subatomic levels.

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