  Quantum Clifford Algebras (QCA), i.e. Clifford Hopf gebras based on bilinear
forms of arbitrary symmetry, are treated in a broad sense. Five alternative
constructions of QCAs are exhibited. Grade free Hopf gebraic product formulas
are derived for meet and join of Grassmann-Cayley algebras including co-meet
and co-join for Grassmann-Cayley co-gebras which are very efficient and may be
used in Robotics, left and right contractions, left and right co-contractions,
Clifford and co-Clifford products, etc. The Chevalley deformation, using a
Clifford map, arises as a special case. We discuss Hopf algebra versus Hopf
gebra, the latter emerging naturally from a bi-convolution. Antipode and
crossing are consequences of the product and co-product structure tensors and
not subjectable to a choice. A frequently used Kuperberg lemma is revisited
necessitating the definition of non-local products and interacting Hopf gebras
which are generically non-perturbative. A `spinorial' generalization of the
antipode is given. The non-existence of non-trivial integrals in
low-dimensional Clifford co-gebras is shown. Generalized cliffordization is
discussed which is based on non-exponentially generated bilinear forms in
general resulting in non unital, non-associative products. Reasonable
assumptions lead to bilinear forms based on 2-cocycles. Cliffordization is used
to derive time- and normal-ordered generating functionals for the
Schwinger-Dyson hierarchies of non-linear spinor field theory and spinor
electrodynamics. The relation between the vacuum structure, the operator
ordering, and the Hopf gebraic counit is discussed. QCAs are proposed as the
natural language for (fermionic) quantum field theory.
