  We apply quantum field theory in quantum space-time techniques to study the
Casimir effect for large spherical shells. As background we use the recently
constructed exact quantum solution for spherically symmetric vacuum space-time
in loop quantum gravity. All calculations are finite and one recovers the usual
results without the need of regularization or renormalization. This is an
example of how loop quantum gravity provides a natural resolution to the
infinities of quantum field theories.
