Noncommutative physics on Lie algebras, Z_2^n lattices and Clifford algebras

Details Noncommutative physics on Lie algebras, Z_2^n lattices and Clifford algebras Noncommutative physics on Lie algebras, Z_2^n lattices and Clifford algebras

2003-02-16

arxiv.org/abs/hep-th/0302120v2

Physics

High Energy Physics

High Energy Physics - Theory

Final version to appear in Clifford Algebras: Application to Mathematics, Physics, and Engineering, ed. R. Ablamowicz, Birkhau

Scientific paper

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, $\theta$-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.

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