Course

This course is aimed at advanced undergraduate and beginning graduate students, and is inspired by a book by the same title, written by Padmanabhan. Each session consists of solving one or two pre-determined problems, which is done by a randomly picked student. While the problems introduce various subjects in Astrophysics and Cosmology, they do not serve as replacement for standard courses in these subjects, and are rather aimed at educating students with hands-on analytic/numerical skills to attack new problems.

At first sight, the ERG does not sit well with gauge theories: a naive implementation of the momentum cutoff central to the ERG breaks gauge invariance. However, things are not as they seem. Not only is it possible to construct a gauge invariant cutoff, but it is possible to construct manifestly gauge invariant ERGs. I will discuss the formulation, what has been achieved to date, and what can reasonably be hoped for in the future.

One of the main strengths of the ERG is that it admits nonperturbative approximation schemes which preserve renormalizability. I will introduce a particularly powerful scheme, the derivative expansion.