## Chapter 5Scaling and transformation groups. Renormalization group

### 5.1 **Dimensional analysis and transformation groups**

We recall the definition of a transformation group. Suppose we have a set of transformations with *k* parameters,

where the *f*_{v} are smooth functions of their arguments in a certain domain. We say that this set forms a *k*-parameter group of transformations if the following conditions are satisfied.

1. Among the transformations (5.1) there exists the identity transformation.

2. For each transformation of the set (5.1) there exists an inverse transformation that also belongs to the set (5.1).

3. For each pair of transformations ...