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

Journal Article · Mon Jul 15 00:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4809939· OSTI ID:22218265

Varshovi, Amir Abbass ^[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)

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.

• OSTI ID: 22218265
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 7; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
CLASSIFICATION
COMMUTATION RELATIONS
QUANTUM FIELD THEORY