Anyone know how to begin learning QFT?

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SUMMARY

Quantum Field Theory (QFT) is a complex framework that integrates special relativity with quantum mechanics, requiring a solid understanding of several foundational topics. Key prerequisites include many-body quantum theory, statistical mechanics, and relativistic quantum mechanics, particularly the Dirac and Klein-Gordon equations. Essential concepts such as gauge theories, quantum electrodynamics (QED), and quantum chromodynamics (QCD) are also crucial. A strong grasp of second quantization and renormalization techniques is necessary for dealing with interacting systems in QFT.

PREREQUISITES
  • Many-body quantum theory
  • Statistical mechanics
  • Relativistic quantum mechanics (Dirac equation, Klein-Gordon equation)
  • Gauge theories (QED, QCD)
NEXT STEPS
  • Study many-body quantum theory fundamentals
  • Learn about statistical mechanics and its applications in field theory
  • Explore relativistic quantum mechanics, focusing on the Dirac and Klein-Gordon equations
  • Investigate second quantization and renormalization techniques in quantum field theory
USEFUL FOR

Undergraduate physics students, aspiring theoretical physicists, and anyone seeking to understand the foundational concepts leading to Quantum Field Theory.

korea_mania
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I am currently a final year undergrad trying to understand Quantum field theory. However, the correct pathway to reach QFT is not so obvious.

Topics like many-body quantum theory, statistical mechanics, relativistic quantum mechanics keep showing up. Some field theory books introduce QFT as the correct framework to combine special relativity and quantum mechanics. Some particle physics books introduce QED and QCD together with the notion of gauge theories and lie group. Some statistical mechanics book will introduce the method of second quantization and renormalization to deal with the interacting system.

1. If QFT is indeed a relativistic version of quantum theory, how about relativistic quantum mechanics such as the Dirac equation and Klein-Gordan equation?
2. If QFT has to deal with a large number of degrees of freedom, is statistical mechanics and statistical field theory required before touching any QFT?
3. If QFT is treating all kind of particles as some kind of excitation of the corresponding fields, is it simply the application of the modern quantum theory on all the other quantum systems?

Can anyone just give me a clear definition of ''many-body quantum theory'', ''relativistic quantum mechanics'', ''quantum field theory''? And also, where should I begin?
 
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I think you should begin by learning undergrad physics. As you point out, QFT builds upon a broad foundation. You want to have that foundation rock solid.
 

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