Instructor: Oliver Rosten, Dublin Institute for Advanced Study
Type: Perimeter Institute non-credit course
Dates: April 16 - May 7, every Wednesday from 10:30 am - 11:30 am
Location: Perimeter Institute, Bob Room

Lecture 1: Wilsonian Renormalization
 
In this lecture, I will discuss Wilson's picture of renormalization and its relation to the Exact Renormalization Group (ERG). In particular, I will focus on how one can understand, in a physically intuitive way, what it is for a quantum field theory to be nonperturbatively renormalizable.
 
Lecture 2: Exact Renormalization Group Equations
 
I will show how to construct very general ERG equations, and will use this as the starting point for a discussion of Polchinski's equation and its cousins. I will introduce diagrammatics and an associated universal calculus, which will be illustrated with a simple calculation.
 
Lecture 3: The derivative Expansion
 
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.
 
Lecture 4: Gauge Theories
 
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.