2003/02/16 by Shahn Majid, S. Majid, Majid, S.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #advanced mathematical theories #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.hep-th/0302120
Final version to appear in Clifford Algebras: Application to Mathematics, Physics, and Engineering, ed. R. Ablamowicz, Birkhauser (2003); added a couple of references and fixed typos (no significant revision). 24 pages, 1 .eps figure
openalex publication_date 2003/02/16 · arxiv created 2003/10/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We survey noncommutative spacetimes with coordinates being enveloping algebras of Lie algebras. We also explain how to do differential geometry on noncommutative spaces that are obtained from commutative ones via a Moyal-product type cocycle twist, such as the noncommutative torus, θ-spaces and Clifford algebras. The latter are noncommutative deformations of the finite lattice (\Z2)n and we compute their noncommutative de Rham cohomology and moduli of solutions of Maxwell's equations. We exactly quantize noncommutative U(1)-Yang-Mills theory on \Z2×\Z2 in a path integral approach.