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Various combinatorially non-local field theories are known to berenormalizable. Still, explicit calculations of amplitudes are very rare andrestricted to matrix field theory. In this contribution I want to demonstratehow the BPHZ momentum scheme in terms of the Connes-Kreimer Hopf algebraapplies to any combinatorially non-local field theory which is renormalizable.This algebraic method improves the understanding of known results innoncommutative field theory in its matrix formulation. Furthermore, I use it toprovide new explicit perturbative calculations of amplitudes in tensorial fieldtheories of rank $r>2$.

Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme