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Title: Groenewold-Moyal product, α*-cohomology, and classification of translation-invariant non-commutative structures

The theory of α*-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.
Authors:
 [1]
  1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM) and School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran (Iran, Islamic Republic of)
Publication Date:
OSTI Identifier:
22218265
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 7; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; CLASSIFICATION; COMMUTATION RELATIONS; QUANTUM FIELD THEORY