What is the ladder approximation and how does it work?

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SUMMARY

The ladder approximation is a technique used in statistical field theory and condensed matter physics, specifically related to the summation of certain Feynman diagrams. It is essential for understanding complex interactions in many-body problems. The book "A Guide to Feynman Diagrams in the Many-Body Problem" by R. Mattuck, particularly chapter 10, provides a comprehensive explanation of this approximation, including its applications and limitations. Additionally, Gross's work on relativistic quantum mechanics and field theory also addresses this topic.

PREREQUISITES
  • Understanding of Feynman diagrams
  • Familiarity with many-body quantum mechanics
  • Knowledge of Dyson's equation
  • Basic concepts of renormalization
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  • Read "A Guide to Feynman Diagrams in the Many-Body Problem" by R. Mattuck
  • Study Dyson's equation and its applications in field theory
  • Explore renormalization techniques in quantum mechanics
  • Investigate the implications of the ladder approximation in condensed matter physics
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Researchers, graduate students, and professionals in theoretical physics, particularly those focusing on statistical field theory and condensed matter physics.

ledamage
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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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The book of Gross (relativistic quantum mechanics and field theory) covers it I think
 
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.
 

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