Statistical Mechanics, Critical Phenomena and Renormalization Group
An introduction to the methods of statistical mechanics that evolves into critical phenomena and the renormalization group.
The analogy between statistical field theory and quantum field theory is addressed throughout the course.
The key concept emphasized in this course is universality; we are concerned with systems with a large number of degrees of freedom which may interact with each other in a complicated and possibly highly non-linear manner, according to laws which we may not understand. However, we may be able to make progress in understanding the behavior of such problems by identifying a few relevant variables at particular scales. The renormalization group addresses such a mechanism.
Some selected topics are covered, such as conformal field theory, vector models/matrix models, and SLE.
Classical Mechanics and Quantum Mechanics to advanced undergraduate level