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The basics idea

There follows a simple description of the ERG. For a more technical discussion, click here.

The basic idea of the ERG is very familiar from everyday experiences: the way in which we describe the world around us depends on the scale at which we observe it. For example, suppose that you were asked to describe the world around you. Although it is always the same thing that it being described, the description would be radically different depending on whether you were For example, if looking at the Earth from space, it would be described in terms of oceans and continents; but looking through a microscope the description would be in terms of very different things. In more technical language, the degrees of freedom relevant to different scales change with the scale.

Separating out what is relevant at one scale from what is relevant at a different scale is a very useful way of decomposing hard problems into easier problems. The mathemetical formalism that allows us to do this is the ERG.

Technical Description

The Exact Renormalization Group (ERG) is essentially the continuous version of Wilson's RG. Thus, having defined a bare Lagrangian at the bare scale, we integrate out degrees of freedom between this scale and a lower, effective scale. This is done in such a way that the partition function (and hence the physics) is unchanged. The Exact Renormalization Group Equation (ERGE) states how the effective action changes with the effective scale. This equation is defined nonperturbatively and its solution would amount to the solution of the field theory in question. Needless to say, it is only known how to do this in very special circumstances!

The ERG provides a very powerful framework for dealing with renormalization and possesses a number of particular assets:

Last modified: Thu Jan 10 2008