Homepage for C6 - Theoretical Physics (Hilary Term 2023)

C6 Coordinator and Hilary Term Lecturer: Andrei Starinets (andrei.starinets@physics.ox.ac.uk)

Lectures in HT-2023 will be in person according to the standard C6 schedule, all in Dennis Sciama Lecture Theatre, DWB, Department of Physics.

Old lectures can be found online (on Canvas) (pre-recorded). The handwritten notes they are based on (as well as the more comprehensive LaTeX-typed notes) are available below.

Tutorial classes are in weeks 4, 6, 8. Problem sheets are available below. The schedule and the tutorial groups list will be available soon.

HT-2023 Topics

1. Classical field theory

2. Symmetries of the action. Noether's theorem

3. Spontaneous symmetry breaking. Goldstone's theorem

4. Canonical quantization of fields

5. Interacting quantum fields

6. Feynman diagrams

7. Path integrals in quantum field theory

8. Examples of interacting quantum field theories

Lecture Notes

1. Classical Field Theory

2. Canonical Quantisation

3. Interacting Quantum Fields

4. Path Integrals

Handwritten Lecture Notes

Lecture 1 [Introduction and motivation. Planck units. When do we need QFT? Inadequacy of single-particle relativistic wave equations. Success of QED.]

Lecture 2 [Causality in relativistic quantum theory. Electromagnetic field as Hamiltonian system.]

Lecture 3 [Classical field theory. Euler-Lagrange field equations. Scaling dimensions of fields. Examples of Lagrangians.]

Lecture 4 [Symmetries and conservation laws. Noether's theorem (for symmetries involving transformation of fields only).]

Lecture 5 [First Noether's theorem (general case). Energy-momentum tensor. Second Noether's theorem.]

Lecture 6 [Spontaneous breaking of continuous global symmetry. Goldstone's theorem in classical field theory.]

Lecture 7 [Canonical quantisation of fields. Example of a free real scalar field. Normal ordering. The cosmological constant problem. Single and multi-particle states.]

Lecture 8 [Two-point functions: Pauli-Jordan, Feynman, retarded, advanced, and more. Their explicit form (for the case of a free real scalar field). Connection to Green's functions of relevant differential operators.]

Lecture 9 [Quantum (free) complex scalar field. Interacting quantum fields. Interaction picture. Dyson formula for the S-matrix.]

Lecture 10 [Wick's theorem. Feynman diagrams. Examples.]

Lecture 11 [Leading order 2->2 amplitude in the scalar Yukawa theory. Mandelstam variables. LSZ reduction formula.]

Lecture 12 [Decay rates and cross-sections. Examples. One-loop integrals and ultraviolet divergences (example). Coupling "constant" dependence on energy.]

Lecture 13 [Path integrals in QFT. The generating functional for N-point functions. Example: the generating functional in a free theory.]

Lecture 14 (Final) [The generating functional for interacting fields. Leading order diagrams for the two-point function (example). Effective action and effective potential.]