Advanced quantum field theory

FaculteitFaculty of Science

NiveauMaster

Studiejaar2026-2027

Beschrijving

Course goals

Course goals

* Familiarity with generating functionals in the path integral formulation

* A basic understanding of both abelian and non-abelian gauge theory, including fundamentals of gauge fixing in path integrals and ghost fields.

* A basic understanding of renormalization in QFT, including Wilsonian RG and the practical use of counterterms.

* A basic understanding of symmetries (in the path integral formulation), including Ward-Takehashi identities.

* A conceptual understanding of spontaneous symmetry breaking and the Higgs mechanism

* Exposure to some more advanced topics, including anomalies and instantons (to be determined based on time constraints).

* Ability to perform computations in the above areas, and to present your work coherently and professionally, in preparation for research in high-energy theory.

Content

This course (AQFT) covers a number of advanced topics in quantum field theory, some of which are often covered in “QFT II/III” courses. It assumes familiarity with the path integral formulation of QFT, and hence requires the QFT course as a prerequisite. After a brief review of path integrals and generating functionals, we will systematically introduce abelian gauge theory, including the Faddeev-Popov prescription, and then generalize to non-abelian gauge theory. Relevant mathematical concepts, such as fibre bundles and Lie groups, will be introduced when needed. We will then discuss renormalization in some detail, including its conceptual underpinnings in Wilsonian RG and the perturbative application via counterterms, with appropriate regularization schemes. We then move on to a selection of more advanced topics, including a discussion of symmetries and conservation laws at the quantum level, the important concept of spontaneous symmetry breaking, anomalies, and instantons (final topic list to be confirmed based on time constraints).

Note there is some superficial topical overlap with Field Theory in Particle Physics (FTPP), but the focus of this course is more formal rather than applied, and the approach will often be more mathematically oriented. In particular, we will work in the path integral formulation, and considerable attention is devoted to conceptual underpinnings. Conversely however, there will be no discussion of particle phenomenology or the Standard Model, so students interested in particle physics are encouraged to consider FTPP. Taking both courses is also fine, and may provide a more well-rounded exposure to the material.

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