What mathematics books need to read ?

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SUMMARY

To effectively understand Quantum Field Theory as presented in Steven Weinberg's volumes 1, 2, and 3, a solid foundation in group theory is essential. The recommended resource for representation theory is "Lie Groups, Lie Algebras, and Some of Their Applications" by Robert Gilmore, which provides a comprehensive overview. It is crucial to avoid abstract algebra books that concentrate on finite groups, as they do not align with the requirements of Quantum Field Theory.

PREREQUISITES
  • Understanding of Quantum Field Theory concepts
  • Familiarity with group theory fundamentals
  • Basic knowledge of representation theory
  • Awareness of the limitations of abstract algebra in the context of QFT
NEXT STEPS
  • Study "Lie Groups, Lie Algebras, and Some of Their Applications" by Robert Gilmore
  • Research advanced topics in representation theory
  • Explore the mathematical foundations of Quantum Field Theory
  • Investigate the differences between finite and infinite groups in physics
USEFUL FOR

Students and researchers in theoretical physics, particularly those focusing on Quantum Field Theory and its mathematical underpinnings, will benefit from this discussion.

fxdung
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What is mathematics books need to read to well understand Quantum Field Theory of Weinberg Vol 1,2,3?Please hint me some group theory books?I know not much in representation of group.
 
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If you're interested in representation theory, then you can't really do better than Hall: https://www.amazon.com/dp/0387401229/?tag=pfamazon01-20
Do not get an abstract algebra book. Those books focus a lot on finite groups, which are things which you won't need for QFT.
 
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