twisted, $F^{\mu\nu}_\theta~=~F^{\mu\nu}_0$. But covariant derivatives of matter fields $\phi_\theta$ are twisted: $(D_\mu\phi)_\theta~=~
    (D_\mu\phi)_0~e^{\frac{1}{2}{\overleftarrow{\partial}}\wedge
    P}$. where $(D_\mu\phi)_0$ is the untwisted covariant derivative of the untwisted $\phi_0$. Thus in correlators $W_N^\theta$, we must use $(D_\mu\phi)_\theta$ for matter fields, $F^{\mu\nu}_0$ for Yang-Mills tensor.

-   There are ambiguities in formulating scattering theory. Thus if we substitute (\[phiin\]) directly in the LHS of (\[LSZformula\]), we get our earlier result [@07081379]. This corresponds to putting the twist factor in (\[twist\]) outside the symbol T in (\[GNtheta\]). At this moment, lacking a rigorous scattering theory, we do not know which of these is the correct answer. In this connection, we must mention the important work of Buchholz and Summers[@buchholz] which rigorously develops the wedge localisation ideas of Grosse and Lechner to establish a scattering theory for two incoming and two outgoing particles. The result resembles those in our earlier approach[@bpq], but there seem to be descrepencies in the signs of the momenta in the overall phases.

For calculating (\[ncLSZ\]), we need a formalism for doing perturbation theory to calculate Wightman functions. Once we have that, we can calculate the time-ordered product by writing it in terms of Wightman functions and twist factors. We show such a calculation 