Advanced Quantum Theory IV

The course will introduce Quantum Field Theory (QFT) by bringing together concepts from classical Lagrangian and Hamiltonian mechanics, quantum mechanics and special relativity. We will also introduce string theory, both as a simple two-dimensional QFT and as a way to go beyond QFT concepts.

The course will begin with a reminder of classical field theory concepts. We then go on to a discussion of free and interacting quantum field theories in the operator formalism, explain Feynman diagrams and the computation of scattering amplitudes. In the second term, we begin with an explanation of path integrals, both in quantum mechanics and quantum field theory. String theory follows next, and we will discuss its spectrum, symmetries and duality symmetries. The last part of the course is about scale dependence and renormalisation.

You are strongly encouraged to consult some of the recommended books, and especially the problems in them, in addition to these lecture notes.

Other homework problems (including the ones to be handed in for marking) can be found in the lecture notes.

• Artu Rajantie's Advanced Quantum Field Theory at Imperial College.
• David Tong's Lectures on Quantum Field Theory at Cambridge.
• Michael Luke's Quantum Field Theory lecture notes at Toronto.
• Sidney Coleman's '75-'76 Harvard lectures as nostalgic black and white video recordings.

 

The lecture notes give rough indications of the content of a lecture of two hours; divide in two parts to estimate what I will do in each one-hour lecture. Thursday lectures in CG218, Friday lectures in E005.

week	day	content
1	Thursday October 6	Overview, literature
2	Friday October 7	Relativistic invariance
3	Thursday October 13	Hamiltonian and Langrangian methods
4	Friday October 14	Functional derivatives interlude
5	Thursday October 20	Noether's theorem
5	Friday October 21	Multi-particle quantum mechanics
6	Thursday October 27	Canonical quantisation
6	Friday October 28	Anti-particles, propagators