Advanced mathematics in theoretical physics

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Discussion Overview

The discussion revolves around seeking advanced mathematical references applicable to theoretical particle physics. Participants share suggestions for books that cover various aspects of mathematical physics, particularly in the context of quantum theory and field theory.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant requests recommendations for advanced mathematical physics references beyond Howard Georgi's work on Lie Algebras in particle physics.
  • Another participant asks for clarification on the specific areas of interest within theoretical physics to provide more targeted suggestions.
  • A suggestion is made for Varadarajan's "Geometry of Quantum Theory" as a challenging resource.
  • Multiple participants recommend the three books by Zeidler for a comprehensive overview of mathematical physics in quantum field theory.
  • Further recommendations include a five-volume mathematical physics encyclopedia and several other advanced texts, such as those by Prakash, Emch, and Thirring, while noting that these may be lengthy or expensive.
  • There is an indication that if the requester seeks something more specific, such as advanced texts on Lie algebras, they should clarify their needs.

Areas of Agreement / Disagreement

Participants generally agree on the value of the suggested texts, but there is no consensus on a single recommendation, as various perspectives on the appropriateness of the books are presented.

Contextual Notes

Some suggestions may depend on the specific mathematical topics of interest, and the discussion does not resolve which texts are definitively the most suitable for the requester's needs.

PaulDirac
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Hi everyone,

Please refer me to a very advanced mathematical physics reference that has applications in theoretical particle physics. I have seen the book Howard Georgi in Lie Algebras in particle physics but want more advanced ones. Any ideas would be very appreciated.Paul
 
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Theoretical physics is a vast subject. More precisely, what are you looking for ?
 
For a very wide panorama of mathematical physics in quantum field theory see the 3 books by Zeidler
https://www.amazon.com/dp/3540347623/?tag=pfamazon01-20
https://www.amazon.com/dp/3540853766/?tag=pfamazon01-20
https://www.amazon.com/dp/3642224202/?tag=pfamazon01-20
each having more than 1000 pages.

An even wider scope is given in the 5-volume mathematical physics encyclopedia
https://www.amazon.com/dp/0125126603/?tag=pfamazon01-20

If these are too big or two expensive for you, then somewhat shorter (but still quite advanced with a wide scope) are

Prakash
https://www.amazon.com/dp/1860943659/?tag=pfamazon01-20

Emch
https://www.amazon.com/dp/0444557946/?tag=pfamazon01-20

and the 2 books by Thirring
https://www.amazon.com/dp/0387406158/?tag=pfamazon01-20
https://www.amazon.com/dp/3540430784/?tag=pfamazon01-20

All those are quite general books, but if you want something more specific (e.g. a more advanced text on Lie algebras in particle physics), then you should specify.
 
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