1210.1004 (Amir Abbass Varshovi)

Groenewold-Moyal Product, α^\star-Cohomology, and Classification of
Translation-Invariant Non-Commutative Structures    [PDF]

Amir Abbass Varshovi

\alpha^\star-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translation-invariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory.

View original: http://arxiv.org/abs/1210.1004