Symmetries in physics

INSTRUCTOR: Predrag Cvitanović
ROOM: online

COURSE DESCRIPTION: Graduate level introduction to modern theoretical physics and mathematics techniques for study of symmetries, with applications to quantum mechanical and dynamical systems.

A detailed overview :

It is a course that is offered infrequently, but if you are working on a problem in

astrophysics, particle physics, general relativity, exoplanets, black holes, AM&O, many-body physics, quantum systems, BECs, atomic physics, condensed matter, graphene, nanostructures, mesoscopic physics, neutron and x-ray diffraction, quantum transport, surface and materials physics, nonlinear physics, chaos, nonchaotic orbits, synchronization, fluid dynamics, PoLS, soft matter, topological metamaterials, symmetry-restrained flexing, systems biology, genome, locomotion, robophysics, virtual reality, life and death, or theoretical physics,

and your problem exhibits a symmetry, do not bother bugging me about it unless you take this course. If you take it, I would love to learn about your problem - that's the only reason for teaching it, the pleasure of learning physics. With symmetries in physics comes much magic, and even a humble plumber's task such as understanding flow in a pipe requires a deep, and for a plumber often nonintuitive grasp of symmetries. Turns out, if anyone was born knowing why character matters, I have not met her yet.

To fix your plumbing problem, you need the basic tools of group theory that nobody ever teaches you: finite groups, subgroups, cosets, and conjugacy, group of permutations, matrix representations, tensors, Schur’s Lemma, characters and character table construction, irreducible representations, Lie groups, rotations, and why you need no Clebsch-Gordon coefficients.

The course is aimed at phd students, postdoctoral fellows and advanced undergraduates in physics, mathematics, chemistry and engineering.

Your professor does not know this fancy footwork. Make her proud.

P. Cvitanović, Group Theory  - course textbook, available on
B. Gutkin, Group theory and its applications in physics
W. G. Harter, Principles of Symmetry, Dynamics, and Spectroscopy.
Dresselhaus, Dresselhaus and Jorio, Group Theory: Application to the Physics of Condensed Matter