  We exhibit a Hopf superalgebra structure of the algebra of field operators of
quantum field theory (QFT) with the normal product. Based on this we construct
the operator product and the time-ordered product as a twist deformation in the
sense of Drinfeld. Our approach yields formulas for (perturbative) products and
expectation values that allow for a significant enhancement in computational
efficiency as compared to traditional methods. Employing Hopf algebra
cohomology sheds new light on the structure of QFT and allows the extension to
interacting (not necessarily perturbative) QFT. We give a reconstruction
theorem for time-ordered products in the spirit of Streater and Wightman and
recover the distinction between free and interacting theory from a property of
the underlying cocycle. We also demonstrate how non-trivial vacua are described
in our approach solving a problem in quantum chemistry.
