The Exact Renormalization Group

A series of four lectures exploring the Exact Renormalization Group. This non-credit mini course will be offered at Perimeter Institute between April 16 and May 7 2008.

 

Wednesday May 07, 2008
Speaker(s): 

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.

 

Wednesday Apr 30, 2008
Speaker(s): 

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.

 

Wednesday Apr 23, 2008
Speaker(s): 

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.

 

Wednesday Apr 16, 2008
Speaker(s): 

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.