  Renormalization is one of the deepest ideas in physics, yet its exact
implementation in any interesting problem is usually very hard. In the present
work, following the approach by Glazek and Maslowski in the flat space, we will
study the exact renormalization of the same problem in a nontrivial geometric
setting, namely in the two dimensional hyperbolic space. Delta function
potential is an asymptotically free quantum mechanical problem which makes it
resemble non-abelian gauge theories, yet it can be treated exactly in this
nontrivial geometry.
