Noncommutative physics on Lie algebras, Z_2^n lattices and Clifford algebras
Abstract
Description
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 $(\Z_2)^n$ 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 $\Z_2\times\Z_2$ in a path integral approach.
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
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