Fubctional integral approach to quantum gauge theories on a noncommutative space-time

We propose a construction of actions of a quantum gauge field theory on a noncommutative space-time, based on a Fourier transform on the Doplicher-Fredenhagen-Roberts group. This approach leads to a functional integral representation of the action, which in turn leads to considering the space of probability measures on the classical space-time as a noncommutative version of the space-time. This approach allows a very natural treatment of gauge fields terms in the action.