alpha^star-Cohomology and Classification of Translation-Invariant   Non-Commutative Quantum Field Theories
  Translation-invariant products are studied in the setting of alpha^star-cohomology. It is explicitly shown that all quantum behaviors including the Green's functions and the scattering matrix of translation-invariant non-commutative quantum field theories are thoroughly characterized by alpha^star-cohomology classes of the star products. 
Amir Abbass Varshovi
math-ph hep-th math.MP