We construct a quantum field theory in noncommutative spacetime by twisting the algebra of quantum operators (especially, creation and annihilation operators) of the corresponding quantum field theory in commutative spacetime. The twisted Fock space and S-matrix consistent with this algebra have been constructed. The resultant S-matrix is consistent with that of Filk [37]. We find from this formulation that the spin-statistics relation is not violated in the canonical noncommutative field theories.

We twist the Hopf algebra of igl(n, R) to obtain the κ-deformed spacetime coordinates. Coproducts of the twisted Hopf algebras are explicitly given. The κ-deformed spacetime obtained this way satisfies the same commutation relation as that of the conventional κ-Minkowski spacetime, but its Hopf algebra structure is different from the well known κ-deformed Poincaré algebra in that it has larger symmetry algebra than the κ-Minkowski case. There are some physical models which consider this symmetry [42,43,44]. Incidentally, we obtain the canonical (θ-deformed) non-commutative spacetime from canonically twisted igl(n, R) Hopf algebra.

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