Noncommutative field theory from twisted Fock space

We construct a quantum field theory in noncommutative space time by twisting the algebra of quantum operators (especially, creation and annihilation operators) of the corresponding quantum field theory in commutative space time. The twisted Fock space and $S$-matrix consistent with this algebra have been constructed. The resultant $S$-matrix is consistent with that of Filk [Tomas Filk, Phys. Lett. B 376, 53 (1996).]. We find from this formulation that the spin-statistics relation is not violated in the canonical noncommutative field theories.

Figure 1

Illustration of the notation for momenta $\tilde{\alpha }$ and $\tilde{\beta }$.