  Braided quantum field theories proposed by Oeckl can provide a framework for
defining quantum field theories having Hopf algebra symmetries. In quantum
field theories, symmetries lead to non-perturbative relations among correlation
functions. We discuss Hopf algebra symmetries and such relations in braided
quantum field theories. We give the four algebraic conditions between Hopf
algebra symmetries and braided quantum field theories, which are required for
the relations to hold. As concrete examples, we apply our discussions to the
Poincare symmetries of two examples of noncommutative field theories. One is
the effective quantum field theory of three-dimensional quantum gravity coupled
with spinless particles given by Freidel and Livine, and the other is
noncommutative field theory on Moyal plane. We also comment on quantum field
theory on kappa-Minkowski spacetime.
