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

Thürigen, J

Zusammenfassung

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

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