  Following up the work of [1] on deformed algebras, we present a class of
Poincar\'e invariant quantum field theories with particles having deformed
internal symmetries. The twisted quantum fields discussed in this work satisfy
commutation relations different from the usual bosonic/fermionic commutation
relations. Such twisted fields by construction are nonlocal in nature. Despite
this nonlocality we show that it is possible to construct local interaction
Hamiltonians which satisfy cluster decomposition principle and are Lorentz
invariant. We further illustrate these ideas by considering global SU(N)
symmetries. Specifically we show that twisted internal symmetries can
significantly simplify the discussion of the marginal deformations
(\beta-deformations) of the N=4 SUSY theories.
