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Advanced Quantum Field Theory - MAT00081M

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  • Department: Mathematics
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2022-23

Module summary

Building on the Quantum Field Theory module, this module introduces three topics in advanced quantum field theory, each of which is connected to important areas of research.

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Module will run

Occurrence Teaching period
A Spring Term 2022-23

Module aims

Building on the Quantum Field Theory module, this module introduces three topics in advanced quantum field theory, each of which is connected to important areas of research.

Module learning outcomes

Subject content

The module consists of three topics in advanced quantum field theory, of 6 lectures each.  At the end of the module, a student will know and understand the key ideas of each topic and be able to solve unseen problems using these methods. They will also have an appreciation of the wider context and significance of the content.

 

Academic and graduate skills

  • Academic skills: the topics and methods taught are central in research in Quantum Field Theory.
  • Graduate skills: through lectures, example classes, students will develop their ability to assimilate, process and engage with new material quickly and efficiently. They develop problem solving-skills and learn how to apply techniques to unseen problems.

Module content

The precise content is subject to change from year to year but will be announced in advance of module choices being made.

Indicative content:

  • Topic 1: Introduction to path integral formulation of quantum mechanics. Applications: perturbative expansions, diagrammatic techniques, semiclassical approximation.
  • Topic 2: Gauge Theory.  Gauge theories are at the foundation of modern particle physics.  In these lectures you will learn how to construct the Lagrangian in Yang-Mills theory and how to quantize it using perturbation theory.  I will focus on the example of quantum mechanics (QFT in 0 dimensions), where I will introduce path integral in Grassmann variables and explain the Fadeev-Popov trick (crucial in quantization of gauge theories).
  • Topic 3: Introduction to classical and quantum conformal field theory.  Topics covered will include: the conformal symmetry group in dimension 2 and above, the Virasoro algebra, the operator product expansion, the conformal Ward identities and some simple examples of two dimensional conformal field theories.  

Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Special assessment rules

None

Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

R Shankar, Principles of Quantum Mechanics, Springer (U 0.123 SHA)
L A Takhtajan, Quantum Mechanics for Mathematicians, American Mathematical Society

S Weinberg, The Quantum Theory of Fields (Vols I&II), Cambridge (U 0.143 WEI)

M Schottenloher, A Mathematical Introduction to Conformal Field Theory, Springer (U 0.14 SCH)


The information on this page is indicative of the module that is currently on offer. The University constantly explores ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary. In some instances it may be appropriate for the University to notify and consult with affected students about module changes in accordance with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.