If you think of a one-parameter group of transformations along a curve in the plane as a (Lie) group, and the tangent vector to the curve as a generator of the curve we can intuitively understand Lie's Third Theorem on how a local Lie algebra generates a global Lie group.
Does this theorem apply for semi-groups? More specifically, does it apply to Wilson's Renormalization group, in other words do the renormalization group equations generate a curve?
(It seems as thought they generate the flow of the coupling parameter
so if so - is that all it is, a mathematical irrelevancy or is there physical meaning?)
I ask to understand whether one can give Wilson's renormalization (semi) group, in the context of the statistical-mechanical partition function, any kind of similar interpretation. If it helps, refer to the 1-dimensional Ising model as an example, thank you.
- "Renormalization Group Theory", Yale 430b/530b "Statistical Methods and Thermodynamics" Lecture Notes http://xbeams.chem.yale.edu/~batista/vaa/
- Bluman "Symmetry and Integration Methods for Differential Equations" P. 37
- Wilson, "Renormalization Group and the Kadanoff Scaling Picture", P. 3177
- Grossco, "Solid State Physics" 2nd Ed. P. 764 (For the Flow Diagram)