Quantum Field Theory of Fundamental Interactions 1102-455A

The course is devoted to quantum field theory and its applications to description of elementary particle interactions. Part 1 of the course focuses on the formulation of the theory from first principles. I discuss the approach based on quantum mechanics of many particles and the complementary approach based on quantization of relativistic fields (both by operator methods and by path integrals). In both approaches I formulate the perturbation expansion leading to Feynman diagrams allowing to compute S matrix elements and off-shell Green's functions. I derive formulae relating S matrix elements to measurable quantities (decay widths, cross sections). I discuss renormalization and the renormalization group. Part 2 of the course is devoted to modern theory of particle interactions based on quantum field theory. I discuss quantization of abelian and nonabelian gauge theories, the structure of quantum electrodynamics, as well as of quantum chromodynamics together with its applications to the physics of strong interactions, spontaneous breaking of global and gauge symmetries, effective field theories and anomalies. Finally I present the Standard Model of elementary interactions and briefly discuss its tests and predictions for rare processes and processes violating CP parity.

Program:
1. Relativistic quantum mechanics of many particle systems. Poincare symmetry and particle states. P, T and C operations.
2. Quantization of relativistic fields. Quantization of systems with constraints.
3. "in" oraz "out" states, S matrix, its unitarity and symmetries.
4. General structure of interactions leading to Poincare covariant S matrices. Field operators causality and antiparticles. Spin - statistics connection.
5. Perturbation expansion, Feynman rules and relation of the S matrix elements to measurable quantities. Fermi theory of weak interactions.
6. Off shell Green's functions and their poles.
7. Formulation of quantum Fidel theory with the help of path integrals. Functional methods. Functionals generating various Green's functions. The effective action and the effective potential.
8. Renormalization and the renormalization group. Critical indices in statistical physics.
9. Abelian and nonabelian gauge field theories and their quantization using the path integral method.
10. Structure of quantum electrodynamics. Ward identities. Infrared problems.
11. Quantum chromodynamics and its applications to the strong interaction physics. Asymptotic freedom and its role in description of the deep inelastic scattering.
12. Exact, spontaneously broken and approximate symmetries. Effective field theories as a description of Goldstone boson interactions on the example of physics of the light mesons (pions).
13. Anomalies
14. Spontaneous breaking of gauge symmetries. The Higgs mechanism.
15. Standard Model of elementary particle interactions. Tests of its electroweak sector. Standard Model prediction for rare processes and the role of strong interaction effects.

Attention: This is a very difficult course. Because of complexity of typical quantum field theory calculations, problems cannot be solved in classes. Instead, students are requested
to solve numerous problems at home. The lecturer offers his help In case of difficulties.

Assessment form: There will be two colloquia (one per semester). To qualify to the final examination (written and oral) students have to collect at least half of the points. There is a possibility of qualifying to the September examination by collecting 66% points from the June written examination. Problems for colloquia and examinations are selected from the home problems. Finally, there is a possibility of splitting the oral examination into two parts.

Description by Piotr Chankowski, April 2007.