Renormalization Group Methods in Statistical Field Theory
Fall 2006 lectures at the Feza Gürsey Institute by Michael Hinczewski
11/01/2007: Problem set #10 and #11 solutions posted (others coming soon).
23/12/2006: Problem set #11 posted.
Renormalization group (RG) theory has been one of the great modern innovations
in physics, a crucial component of both condensed matter and high energy theories. In these
lectures, we describe RG methods for statistical physics systems, starting with classical models of phase transitions and critical phenomena, and ending with quantum theories of interacting fermions. Throughout the lectures, we emphasize a field-theoretic approach to the material, but no prior knowledge of field theory is assumed: we introduce concepts like path integrals, functional derivatives, Feynman diagrams, and fermion coherent states as they are needed. Once we have developed the basic tools, we will see that the RG approach is widely applicable to a variety of problems: as an example, we show how RG provides an elegant derivation of the Landau Fermi-liquid theory of metals, and the BCS instability that leads to superconductivity.
The course will be accessible to advanced undergraduate or graduate students. A familiarity with undergraduate statistical mechanics (i.e. partition functions, thermodynamic potentials) and quantum mechanics are the only prerequisites.
The first lecture will be on Friday, September 22, 2006, 14:00-17:00, at the Feza Gürsey Institute (for directions, click here, or e-mail me at firstname.lastname@example.org). The lectures will be once a week on Fridays, though the day may be changed if there is a major conflict with student schedules.
Weekly problem sets will be the most important component of the course grade (50%). The students are strongly encouraged to work together on the homework, but everyone should write up the solutions individually. There will also be 15-minute weekly quizzes (25%), and a final exam (25%). I will be available for office hours, and if there is student interest, for recitations.
If you have any questions, please e-mail me at email@example.com, or call my office at 216-308-9432.