Module MATH41020: Advanced Quantum Theory

Department: Mathematical Sciences

MATH41020: Advanced Quantum Theory

Tied To

• G1K509: Mathematical Sciences

Pre-requisites

Corequisites

Excluded Combinations

Aims

• The module is intended as an introduction to Quantum Field Theory using strings as a primary example.
• It also develops string theory sufficiently to show that its spectrum includes all elementary particles thus unifying the fundamental forces.

Content

• The syllabus contains: Action principles and classical theory.
• Quantisation of free scalar fields; application to strings.
• Virasoro algebra; string constraints as generators of conformal transformations, representations, central charge.
• Spectra: physical state condition, no-ghost theorem, critical dimension, open strung spectrum. Connection to gauge-theory, non-Abelian gauge symmetry and importance for the Standard Model. Closed string spectrum, connection to Gravity. Compactification.
• Spinning string: gauge-fixed action, Ramond and Neveu-Schwarz boundary conditions, Super-Virasoro algebra, spectrum.
• Dirichlet branes.

Learning Outcomes

• Having studied the module students will know the basic principles of quantum field theory and the role of symmetry in modern particle physics.
• be familiar with the fundamental aspects of string theory (quantisation of free stings, string constraints and their algebraic description, spectrum).
• have been made aware of the connection between string spectra and the Standard Model.

• students will be able to use a variety of highly specialised and advanced technical skills in the area of theoretical elementary particle physics.

• students will have developed the ability to operate in complex and specialised contexts close to the cutting edge of research.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
• Written assignments provide formative practice in the application of logic, rigour and extended discourse.
• Summative examinations assess these elements, the knowledge acquired and the ability to solve complex upreductable and specialised problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment

Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.