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Physics  2012 

alpha^star-Cohomology and Classification of Translation-Invariant Non-Commutative Quantum Field Theories

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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.


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