On second quantization on noncommutative spaces with twisted symmetries

Understand

By application of the general twist-induced star-deformation procedure we translate second quantization of a system of bosons/fermions on a symmetric spacetime in a non-commutative language.

• The procedure deforms in a coordinated way the spacetime algebra and its symmetries, the wave-mechanical description of a system of n bosons/fermions, the algebra of creation and annihilation operators and also the commutation relations of the latter with functions of spacetime; our key requirement is the mode-decomposition independence of the quantum field.
• In a conservative view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind.
• In a non-conservative one, we obtain a covariant framework for QFT on the corresponding noncommutative spacetime consistent with quantum mechanical axioms and Bose-Fermi statistics.