Non Commutative Field Theory on Rank One Symmetric Spaces
  Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary space-time. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is taken to extend such theories to non-flat backgrounds such as solvable symmetric spaces. 
P. Bieliavsky, R. Gurau and V. Rivasseau