Functional Methods in Quantum Field Theory (FMQFT | SPA7024P)

Year: 1 | Semester: B | Level: 4 | Credits: 15

Course organiser: Dr Rodolfo Russo | Course deputy:

Synopsis:

The module will introduce Feynman's path integral formulation of Quantum Mechanics and apply it to study of Quantum Field Theory (QFT). Emphasis will be given to the role of symmetries (Ward identities), the renormalisation group and the idea of effective action. The concept of Wilson's effective action and the different nature of (ir)relevant/marginal terms will be discussed. Simple scalar theories will provide the example where to apply the concepts and the techniques introduced. The course will also touch on some more advanced topics, such as quantum anomalies and conformal field theories.

Aims:

The module will discuss QFT as the common language in theoretical physics to describe both fundamental forces in particle physics and critical condensed matter systems. Students will become familiar with the path integral formulation of QFT, the concept of Green's functions, the use of Berezin integrals for functions with anticommuting (Grassmann) variables. At the end of the module they will be able to use these techniques and apply them to derive Ward identities and discuss the Renormalisation Group equations. Applications and examples relevant to both statistical and particle physics will be discussed.

Outcomes:

Academic Content: A1 - Path integral formalism A2 - Renormalisation group A3 - Symmetries Quantum Field Theories Disciplinary Skills - able to: B1 - Applications of Quantum Field Theory to condensed matter systems B2 - Application of Quantum Field Theory to Particle Physics

Recommended books:

Le Bellac: "Quantum and Statistical Field Theory" Oxford University Press

Amit- Mayor "Field Theory, the renormalisation groups, and critical phenomena". World Scientific