Postgraduate Course: Symmetries of Particles and Fields (PGPH11097)
|School||School of Physics and Astronomy
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Available to all students
|Summary||This course sets out the mathematical concepts - Lie groups, Lie algebras and their representations - needed to understand the role of symmetries in particle physics, along with various physical applications, in particular the Lorentz group and SU(3), explicit and spontaneous symmetry breaking, gauge symmetries and the Higgs mechanism.
- Lie Groups; Unitary and Orthogonal Groups; One Dimensional Groups; Translations and Rotations; Generators; Lie Algebras; Representations; SU(2) and SO(3); Scalars, Vectors and Tensors
- Lorentz Group; Spinors and Vectors; Poincare Group
- Invariant Actions; Spin zero fields; Spin half fields; Chiral Symmetry
- Noether's Theorem; Conserved Charges; Stress-Energy Tensor
- Real Forms; Compact Lie algebras; Killing form; Casimir Operators; Cartan subalgebra; Roots and Weights; Representations of SU(3)
- Internal Symmetry; Isospin; the Quark Model; the Eight-Fold Way; Mesons and Baryons
- Broken Symmetry; Soft Breaking; Spontaneous Symmetry Breakdown; Goldstone's Theorem
- Local Symmetry; Maxwell's equations; Yang-Mills Theory; Higgs' mechanism
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2018/19, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 20,
Summative Assessment Hours 2,
Revision Session Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Hours & Minutes
|Main Exam Diet S2 (April/May)||2:00|
On completion of this course, the student will be able to:
- Understand the concepts underlying the mathematical description of symmetries via groups, algebras and their representations.
- Be able to apply these mathematical tools in the context of particle physics, notably to work with the different representations of the Lorentz group and with local and global SU(N) symmetries.
- Understand the concepts of explicit and spontaneous symmetry breaking and their physical consequences, including the Higgs mechanism for mass generation for a general gauge group.
|Graduate Attributes and Skills
|Course organiser||Dr Brian Pendleton
Tel: (0131 6)50 5241
|Course secretary||Ms Wendy Hisbent
Tel: (0131 6)51 3448