Principles of Quantum Field Theory

Annotation

Quantum field theories emerged from the confluence of quantum mechanics and special relativity, and provide an amazingly accurate theoretical framework for describing the behaviour of subatomic particles and forces. The course introduces students to the basic concepts and techniques of quantum field theory along with the key examples of physically relevant models. In particular, canonical and covariant quantization methods are introduced and illustrated on the examples of bosonic, fermionic, and electromagnetic fields.  Topics covered also include perturbation theory and Feynman diagrams, basics of scattering theory, quantum electrodynamics, Green functions, etc. This course is a necessary prerequisite for nearly all other field theory courses of the program.

Course plan

1. Classical fields and symmetries. The Lorentz and Poincare groups. Variational symmetries and Noether’s theorem. Conserved charges as symmetry generators.
2. Classical Klein-Gordon field. Canonical quantization and Fock space.
3. Dirac field. Spinors and Clifford algebra. Dirac equation.  Charge conjugation and anti-particles. Quantization.
4. Electromagnetic field.  Covariant formulation and gauge symmetry. Helicity and degrees of freedom. Hamiltonian formulation. Quantization in the Coulomb gauge
5. Covariant quantization. Lagrangian of quantum electrodynamics.
6. Quantum mechanics of electron. Gyromagnetic ratio. Inborn magnetic moment of electron.
7. Scattering theory. S-matrix and scattering amplitude. S-matrix of the 4 theory.
8. Quantum electrodynamics. S-matrix and Feynman rules.  Pair annihilation. Compton scattering.
9. Green’s functions and LSZ reduction formalism. Generating functionals. 
10. Effective action. Connected diagrams in the momentum space. Self-energy and vertex function.

Literature

1. M. Peskin, D. Schroeder, An Introduction To Quantum Field Theory.
2. C. Itzykson and J.B. Zube, Quantum Field Theory.
3. S. Weinberg, The Quantum Theory of Fields.