Algebraic Methods of Mathematical Physics
University of Queensland
Area of Study
Algebra, Mathematics, Physics
Taught In English
MATH2000 or MT250
Course Level Recommendations
ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.
Host University Units2
Recommended U.S. Semester Credits4
Recommended U.S. Quarter Units6
Hours & Credits
OverviewCourse DescriptionAlgebraic structures & their representations of importance to current mathematical physics research: Lie algebras & superalgebras; quantum groups & algebras; Hopf & quasi-Hopf algebras; affine & Kac-Moody algebras. Illustrative applications to knot theory.Course IntroductionThis course is an introduction to algebraic methods used in mathematical physics to describe symmetries mathematically and solve problems in quantum mechanics. Focus will be on Lie algebras and their representation theory, but with the aim of developing an understanding of algebraic structures and approaches more generally. Some of the algebraic methodologies will be applied to the non-relativistic hydrogen atom and the isotropic simple harmonic oscillator.Learning ObjectivesAfter successfully completing this course you should be able to:
Class Contact3 Lecture hours, 1 Tutorial hourAssessment SummaryProblem Sets (4): 28%Quizes: 20%Final Exam: 52%
- understand the basics of Lie algebra theory
- characterize a variety of algebraic structures
- work with representations of algebraic symmetries
- apply methodologies of representation theory to the analysis of physical systems
- use the symmetries of certain physical Hamiltonians to determine the energy spectra and degeneracies
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Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.