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Homepage for C6 & AQT - Theoretical Physics & Advanced Quantum Theory

### Coordinator: Andrei Starinets (andrei.starinets@physics.ox.ac.uk)

### Lecturers: Sid (Siddharth) Parameswaran (Michaelmas Term), Andrei Starinets
(Hilary Term)

### Aims and Objectives of the Course

This course covers both the C6 (Theory) MPhys option (in MT & HT) and the MMathPhys Advanced Quantum Theory course (in MT only). The course is intended to give an introduction to some aspects
of classical and quantum field theory, many-body systems and related issues. It also serves as an introduction to the path integral technique. These
form the basis of our current theoretical understanding of
particle physics, condensed matter and statistical physics. An
aim is to present some core ideas and important applications in
a unified way. The applications include classical
mechanics of continuum systems, quantum mechanics and
statistical mechanics of many-particle systems, and some basic
aspects of relativistic quantum field theory.

## Course Structure

MICHAELMAS TERM: Schedule of classes, problem sheets, lecture notes and other materials (Sid Parameswaran)
## MT-2019 Topics

1. Functionals: Mathematical background

2. Path integrals in quantum mechanics

3. Path integrals in quantum statistical mechanics

4. Path integrals and Feynman diagrams

5. Ising model and transfer matrices in 1D

6. 2D Ising model

7. Second quantisation

8. Ideal Fermi gas

9. Weakly interacting bosons

10. Bogliubov excitations and spin waves

11. Spin waves. Path integral for bosons

12. Phase transitions. Ising model and mean-field theory

13. Critical behavior and universality. Landau theory

14. Beyond Landau theory: fluctuations

15. Fluctuations. Other phase transitions

16. Stochastic processes

HILARY TERM: Schedule of classes, problem sheets, lecture notes and other materials (Andrei Starinets)
## HT-2020 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. Path integrals in quantum field theory

6. Interacting quantum fields

5. Feynman diagrams

6. Examples of interacting quantum field theories

## OLD MATERIALS (prior to 2019-2020 academic year)