We give an introductory review of quantum physics on the noncommutative space–time
called the Groenewold–Moyal plane. Basic ideas like star products, twisted statistics, second
quantized fields and discrete symmetries are discussed. We also outline some of the recent
developments in these fields and mention where one can search for experimental signals.

We show that despite the inherent non-locality of quantum field theories on the Groenewold-
Moyal (GM) plane, one can find a class of C, P, T and CPT invariant theories. In particular,
these are theories without gauge fields or with just gauge fields and no matter fields. We
also show that in the presence of gauge fields, one can have a field theory where the
Hamiltonian is C and T invariant while the S-matrix violates P and CPT. In non-abelian
gauge theories with matter fields such as the electro-weak and QCD sectors of the standard …