α *-cohomology, and classification of translation-invariant non-commutative quantum field theories

Abstract

Translation-invariant {star operator} products are studied in the setting of α *-cohomology. It is explicitly shown that all quantum behaviors including Green's functions and the scattering matrix of translation-invariant non-commutative quantum field theories are thoroughly characterized by α *-cohomology classes of the star products. © 2014 Elsevier B.V.