This is the webpage for the lecture series "Unitary representations of spacetime groups" organised by José Figueroa-O'Farrill in the Spring Semester 2024 at the School of Mathematics of the University of Edinburgh.
Relativity groups, such as Poincaré, Galilei or Carroll, act transitively on spacetimes: Minkowski, Galilei or Carroll, respectively. These spacetimes are the arena for the dynamics of classical and quantum particles and fields. Classical particles can be classified via homogeneous symplectic manifolds of the relativity groups, whereas quantum particles (whose wavefunctions are classical fields) are classified by their projective unitary irreducible representations. For the spacetime groups under consideration, these representations can be obtained in at least two ways: geometrically quantising the symplectic manifolds or by Mackey's method of induced representations. This lecture series is about this latter method. The idea is to describe the method in some generality and then to apply it to some interesting examples.
All lectures will take place on Tuesdays at 14:30-16:00 in
JCMB Lecture Theatre A starting on 30
January. There are two exceptions to this rule: there is no
lecture on 20 February (flexible learning week) and the
lecture on 5 March will take place in JCMB Lecture
Theatre BA at the somewhat later time
of 3pm. The format of all lectures will
be two halves of about 40 minutes each with a break in the
middle. I hope to record the lectures and make them available
somehow.
I will place here some references as the lectures progress.