An ultraviolet-finite Hamiltonian approach on the noncommutative Minkowski space

This is an exposition of joint work with S. Doplicher, K. Fredenhagen, and G. Piacitelli on field theory on the noncommutative Minkowski space (2003). The limit of coinciding points is modified compared to ordinary field theory in a suitable way which allows for the definition of so-called regularized field monomials as interaction terms. Employing these in the Hamiltonian formalism results in an ultraviolet finite S-matrix. (Abstract Copyright [2004], Wiley Periodicals, Inc.)