量子場論自學教程

Overture The Universe as a set of harmonic oscillators Lagrangians Simple harmonic oscillators Occupation number representation Making second quantization work Writing down Lagrangians Continuous systems A first stab at relativistic quantum mechanics Examples of Lagrangians, or how to write down a theory III. The need for quantum fields The passage of time Quantum mechanical transformations Symmetry Canonical quantization of fields Examples of canonical quantization Fields with many components and massive electromagnetism Gauge fields and gauge theory Discrete transformations Propagators and perturbations Ways of doing quantum mechanics: propagators and Green’s functions Propagators and Fields The S-matrix Expanding the S-matrix: Feynman diagrams Scattering theory Interlude: wisdom from statistical physics Statistical physics: a crash course The generating functional for fields Path Integrals Path Integrals: I said to him, “You’re crazy” Field Integrals Statistical field theory Broken symmetry Coherent states Grassmann numbers: coherent states and the path integral for fermions VII. Topological ideas Topological objects Topological field theory VIII. Renormalization: taming the infinite Renormalization, quasiparticles and the Fermi surface Renormalization: the problem and its solution Renormalization in action: propagators and Feynman diagrams The renormalization group Ferromagnetism: a renormalization group tutorial Putting a spin on QFT The Dirac equation How to transform a spinor The quantum Dirac field A rough guide to quantum electrodynamics QED scattering: three famous cross sections The renormalization of QED and two great results Some applications from the world of condensed matter Superfluids The many-body problem and the metal Superconductors The fractional quantum Hall fluid Some applications from the world of particle physics Non-abelian gauge theory The Weinberg-Salam model Majorana fermions Magnetic monopoles Instantons, tunnelling and the end of the world Appendix A. Further reading
Appendix B. Useful complex analysis