From wave-mechanics to second quantization on noncommutative spaces withtwisted symmetries

In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the equation of motion in the presence of an external field may look simpler as functions of noncommutative coordinates. It turns out that also the wave-mechanical description of a system of $n$ such bosons/fermions and its second quantization is simplified if we translate them in terms of their deformed counterparts. The latter are obtained by a general twist-induced $\star$-deformation procedure which deforms in a coordinated way not just the spacetime algebra, but the larger algebra generated by an arbitrary number of copies of the spacetime coordinates and by the particle creation and annihilation operators. On the deformed algebra the action of the original spacetime transformations looks twisted. In a non-conservative view, we thus obtain a twisted covariant framework for QFT on the corresponding noncommutative spacetime consistent with quantum mechanical axioms and Bose-Fermi statistics. One distinguishing feature is that the field commutation relations remain of the type ``field (anti)commutator=a distribution''. We illustrate the results by choosing as examples interacting non-relativistic and free relativistic QFT on Moyal space(time)s