Description

Quantum Field Theory is the language of modern physics. Initially introduced in the 1920s and 1930s to reconcile special relativity and quantum mechanics, Quantum Field Theory was developed to describe elementary particles, but it also describes the long distance behaviour of materials in Condensed Matter Physics, it is essential to understand the evolution of the early universe in Cosmology, and it plays a key role in String Theory, our current best attempt to unify the laws of gravitation and of quantum physics.

In this project you will learn the basics of Quantum Field Theory (QFT), focussing on free (that is, non-interacting) quantum fields. While free field theory is typically dismissed as just a boring prerequisite to the study of more interesting interacting quantum field theories, this is far from the truth. In this project you will learn how to formulate and solve free QFTs, and then you will have a chance to explore some of their many fascinating properties and applications: not only how to use calculations in free QFT to learn about quantum field theories with weak interactions, as is done in most beginner QFT courses, but also how to identify the generalised global symmetries of free QFTs, which act on physical observables of different dimensionalities (points, lines, surfaces, ...), how coupling the field theory to sources affects its symmetry properties (aka 't Hooft anomalies), how different-looking QFTs may in fact be equivalent (aka duality), and how free quantum field theories can be used to characterise interesting phases of matter with non-trivial topology and/or unusual non-relativistic spacetime symmetries.

Prerequisite:

Mathematical Physics II (or equivalent)

Corequisite:

Quantum Mechanics III (or equivalent)

Resources

We will draw from some of these resources:

• D. Tong, Quantum Field Theory, Cambridge Part III course, 2006-2007.
• M. Peskin, D. Schroeder, An Inroduction to Quantum Field Theory, Perseus Books, 1995.
• M. Srednicki, Quantum Field Theory, Cambridge University Press, 2007.
• A. Zee, Quantum Field Theory in a nutshell, Princeton University Press, 2003.
• P. Ramond, Field Theory: A Modern Primer, Addison-Wesley, 1989.
• R. Bertlmann, Anomalies in Quantum Field Theory, Oxford University Press, 2000.
• N. Seiberg, Fun with Free Field Theory, PiTP 2015 lecture.
• N. Seiberg, Generalised Global Symmetries, PiTP 2015 lecture.

More references will be available in due course according to your interests.