Modern Quantum Field Theory

Annotation

This is a continuation of the course “Principles of QFT”.  It covers modern and more advanced aspects of the theory. Renormalization techniques will be introduced and applied to the study of important physical phenomena of Quantum Electrodynamics such as the electron self-energy, polarization of vacuum and the anomalous magnetic moment of electron. Path integral formulation of quantum field theory will be developed and applied to quantisation of the so-called non-abelian gauge theories  by modern methods of Faddeev-Popov and the BRST-Symmetry. The basic features of the Standard Model of particle physics such as Spontaneous Symmetry Breaking and the Higgs mechanism also belong to the syllabus. The role of topological solutions in quantum field theory such as monopoles and instantons will also be discussed.

Course plan

1. Renormalization.  Superficial degree of divergence. Dimensional regularization. Renormalization at one loop. Introduction into renormalization group.
2. Radiative corrections in Quantum Electrodynamics (QED). Renormalised QED Lagrangian.  Electron self-energy. Vacuum polarization. β-function of QED and Landau pole.  Anomalous magnetic moment of electron.
3. Path integral in quantum mechanics. Gaussian integrals. Examples. Semi-classical approximation. Stationary phase method.
4. Path integral in field theory. Generating functional of Green’s functions. Functional integral for fermions.
5. Schwinger-Dyson equations.  Ward identities. Wick rotation and relation to statistical mechanics.
6. Non-abelian gauge theories. Yang-Mills theory. Yang-Mills as a constrained Hamiltonian system.
7. Faddeev-Popov covariant quantization. BRST symmetry.
8. Spontaneous symmetry breaking. Vacuum and its symmetries. Goldstone theorem. Higgs phenomenon. Landau-Ginzburg theory. Weinberg-Salam model. The Standard Model of particle physics.
9. Topological solutions. Instantons in Quantum Mechanics. Instantons in Yang-Mills theory.

Literature

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