A geometrical picture of renormgroup
Let be a smooth manifold. Fix a point , and consider the tangent space at this point:
Let us denote this space of trajectories . By the definition of , we have a map:
Lifting tangent vectors to trajectories
Suppose that comes equipped with an action of a Lie algebra , preserving a point .
Then also acts in
Let us try to construct a map
respecting the action of
Does such a map exist?