Fundamental Symmetries (U01428)

? Credit Points : 10 ? SCQF Level : 11 ? Acronym : PHY-5-FundSym

Symmetry principles are now an essential part of our understanding of the underlying structure of physics. The course sets out the mathematical preliminaries - Lie groups, Lie algebras and their representations and covers various physical applications, in particular the Lorentz
group and SU(3), explicit and spontaneous symmetry breaking, gauge symmetries and the Higgs mechanism. Fundamental Symmetries complements the courses on General Relativity, Particle Physics, Quantum Field Theory, and the Standard Model.

Entry Requirements

? Pre-requisites : At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q. Prior attendance at Groups & Symmetries (PHY-4-GroupSym) is desirable. Knowledge of linear algebra is essential.

Variants

? This course has variants for part year visiting students, as follows

Fundamental Symmetries (VS1) (Semester 1 (Blocks 1-2))

Subject Areas

Home subject area

Undergraduate (School of Physics), (School of Physics, Schedule Q)

Delivery Information

? Normal year taken : 5th year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 3 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
21/09/2006	10:00	11:00			Rm 4309 - JCMB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	10:00	10:50	KB
Lecture	Thursday	10:00	10:50	KB

? Additional Class Information : Workshop/tutorial sessions, as arranged.

Summary of Intended Learning Outcomes

After completing this course students should:
1) have a good understanding of Lie Groups and Lie Algebras, and the relationship between them
2) understand the difference between compact and noncompact, and simple and semi-simple Lie Algebras, and the role of the Killing form
3) understand the structure of the Lorentz group, the Poincare group, SU(2) and SU(3)
4) understand the spinor representations the Lorentz group, and how fields correspond to representations of the Poincare group
5) understand how to construct a classical Lagrangian which is invariant under the Poincare group
6) understand the difference between internal and external symmetries, and how to construct theories invariant under local symmetry groups
7) understand the difference between explicit and spontaneous symmetry breaking, and the working of Goldstone's Theorem
8) understand the difference between global and local symmetries, and how to construct a gauge invariant classical Lagrangian
9) understand the working of Higgs' mechanism

In all the above the generic word "understand" is used to mean that the student must be able to use what he has learned to solve a range of unseen problems. The style and level of difficulty of these problems may be found from solving the examples provided in the course. A more complete specification of the material included in the course may be found in the syllabus.