  We consider a massive scalar field living on the recently found exact quantum
space-time corresponding to vacuum spherically symmetric loop quantum gravity.
The discreteness of the quantum space time naturally regularizes the scalar
field, eliminating divergences. However, the resulting finite theory depends on
the details of the micro physics. We argue that such dependence can be
eliminated through a finite renormalization and discuss its nature. This is an
example of how quantum field theories on quantum space times deal with the
issues of divergences in quantum field theories.
