NSCPHD1223 Groups and Algebras in mathematical Physics (GRAMPH)

Volume 2013/2014
Education
MSc Programme in Mathematics
Content
The Fourier transform, Position and Momentum operators, Symmetries in Quantum Mechanics, Projection valued measures, Lie Groups and Lie algebras, Actions of Lie Groups, The Harmonic (metaplectic) representation, Hermite polynomials, The Lorentz, Poincaré, and Conformal Groups. Unitarity. Induced representations and systems of imprimitivity. Quantum groups and Kac-Moody algebras.

Due to the changed format, the course can possibly focus on a few of these topics, depending on the interests of the participants.
Learning Outcome
Knowledge: The student will learn the fundamental results relating to the most basic groups and algebras of mathematics and physics


Competences: The students will obtain a working knowledge of many groups and algebras from mathematical physics as well as generalizations of these.

 

Skills: They will learn how to do computations relating to specifically given groups and algebras. Among the quantities to be determined will be the defining representations, dimensions, actions on sets (manifolds), orbits, and stabilizer subgroups. They will know how to compute the exponential map related to a given matrix Lie group. The students will be able to decide if a given (differential) operator is invariant or equivariant under a given, say, algebra. T Furthermore, they will learn the terminology and basic results realting to the representation theory. They will be able to describe the degeneracy of the spectrum of an invariant operator.

It is a good idea to have seen some kind of measure and integration theory and differential geometry - or to have a maturity that allows one to work directly with new definitions.
Either a reading course, a project course, or both. We will meet once or twice a week as needed.
  • Category
  • Hours
  • Course Preparation
  • 186
  • Lectures
  • 20
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Depending on the chosen format, the student must complete a number of mandatory assignments in a satisfactory way. Possibly after a second hand-in. In the case of a project, a final report must be made, and a presentation thereof given
Aid
All aids allowed
Marking scale
passed/not passed
Censorship form
No external censorship
One internal examiner
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.