Conceptual Issues for Noncommutative Gravity on Algebras and Finite Sets

Details Conceptual Issues for Noncommutative Gravity on Algebras and Finite Sets Conceptual Issues for Noncommutative Gravity on Algebras and Finite Sets

2000-06-20

arxiv.org/abs/math/0006152v1

Int.J.Mod.Phys. B14 (2000) 2427-2450

Mathematics

Quantum Algebra

17 pages, to appear Proc. Euroconference on Noncommutative Geometry and Hopf Algebras in Field Theory and Particle Physics, To

Scientific paper

10.1142/S0217979200001953

We discuss some of the issues to be addressed in arriving at a definitive noncommutative Riemannian geometry that generalises conventional geometry both to the quantum domain and to the discrete domain. This also provides an introduction to our 1997 formulation based on quantum group frame bundles. We outline now the local formulae with general differential calculus both on the base `quantum manifold' and on the structure group Gauge transforms with nonuniversal calculi, Dirac operator, Levi-Civita condition, Ricci tensor and other topics are also covered. As an application we outline an intrinsic or relative theory of quantum measurement and propose it as a possible framework to explore the link between gravity in quantum systems and entropy.

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