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Explore the fundamental principles of relativistic quantum field theory through this comprehensive MIT course taught by Professor Hong Liu. Master the essential concepts and mathematical techniques used to describe elementary particles and condensed matter systems within the framework of special relativity and quantum mechanics. Begin with classical field theories and the principle of locality, then progress through symmetries, conservation laws, and the motivation for quantum field theory. Learn canonical quantization methods for free and complex scalar fields, understand the role of propagators and Green functions, and develop expertise in interacting theories and S-matrix calculations. Delve into path integral formalism for both non-relativistic quantum mechanics and quantum field theory, including time-ordered correlation functions and perturbation theory with Feynman diagrams. Study the Dirac equation in detail, covering its Lorentz covariance, classical solutions, quantization procedures, and various spinor representations including chiral and Majorana spinors. Examine discrete symmetries and fermionic path integrals before advancing to Maxwell theory and its canonical quantization. Conclude with quantum electrodynamics, cross-section calculations, decay rates, elementary QED processes, and an introduction to quantum fluctuations and renormalization theory. Gain practical experience through applications spanning elementary particle physics and condensed matter physics while building a solid foundation for advanced studies in theoretical physics.
