On a Lorentz-invariant interpretation of noncommutative space–time and its implications on noncommutative QFT

By invoking the concept of twisted Poincaré symmetry of the algebra of functions on a Minkowski space–time, we demonstrate that the noncommutative space–time with the commutation relations xμ,xν=iθμν, where θμν is a constant real antisymmetric matrix, can be interpreted in a Lorentz-invariant way. The implications of the twisted Poincaré symmetry on QFT on such a space–time is briefly discussed. The presence of the twisted symmetry gives justification to all the previous treatments within NC QFT using Lorentz invariant quantities and the representations of the usual Poincaré symmetry.