Algebraic Methods of Mathematical Physics

University of Queensland

Course Description

  • Course Name

    Algebraic Methods of Mathematical Physics

  • Host University

    University of Queensland

  • Location

    Brisbane, Australia

  • Area of Study

    Algebra, Mathematics, Physics

  • Language Level

    Taught In English

  • Prerequisites

    MATH2000 or MT250

  • Course Level Recommendations

    Upper

    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.

    Hours & Credits

  • Host University Units

    2
  • Recommended U.S. Semester Credits
    4
  • Recommended U.S. Quarter Units
    6
  • Overview

    Course Description
    Algebraic 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 Introduction
    This 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 Objectives
    After successfully completing this course you should be able to:
    • 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
     
    Class Contact
    3 Lecture hours, 1 Tutorial hour
     
     
    Assessment Summary
    Problem Sets (4): 28%
    Quizes: 20%
    Final Exam: 52%

Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

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.