  Various combinatorially non-local field theories are known to be
renormalizable. Still, explicit calculations of amplitudes are very rare and
restricted to matrix field theory. In this contribution I want to demonstrate
how the BPHZ momentum scheme in terms of the Connes-Kreimer Hopf algebra
applies to any combinatorially non-local field theory which is renormalizable.
This algebraic method improves the understanding of known results in
noncommutative field theory in its matrix formulation. Furthermore, I use it to
provide new explicit perturbative calculations of amplitudes in tensorial field
theories of rank $r>2$.
