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Physics  2012 

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

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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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