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Paper   IPM / Physic / 13068
School of Physics
  Title:   Groenewold-Moyal Product, α^-Cohomology, and Classification of Translation-Invariant Non-Commutative Structures
  Author(s):  A.A. Varshovi
  Status:   Published
  Journal: J. Math. Phys.
  Vol.:  54
  Year:  2013
  Pages:   072301
  Supported by:  IPM
The theory of 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 translationinvariant non-commutative quantum field theory is physically equivalent to a Groenewold- Moyal non-commutative quantum field theory.

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