Time-Space Noncommutativity: Quantised Evolutions
  In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al.. Here we extend it to certain noncommutative versions of the cylinder, $\mathbb{R}^{3}$ and $\mathbb{R}\times S^{3}$. In all these models, only discrete time translations are possible, a result known before in the first two cases. One striking consequence of quantised time translations is that even though a time independent Hamiltonian is an observable, in scattering processes, it is conserved only modulo $\frac{2\pi}{\theta}$, where $\theta$ is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing $a$ and length $L=Na$, only momentum mod $\frac{2\pi}{L}$ is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined. 
A. P. Balachandran, T. R. Govindarajan, A. G. Martins, P.   Teotonio-Sobrinho