Applications to quantum gravity from C*-bundles

Abstract

Applications to quantum gravity of some results in C*-algebras are developed. We open by describing why algebra may be an integral aspect of quantum gravity. By interpreting the inner automorphisms of a C*-algebra as families of parallel transports on a C*-bundle, we define a notion of generalised connection for C*-bundles, implying that C*-bundle dynamical systems can be used to study a Dirac operator's spectrum and also the generator of the modular group. The fact that their dynamics preserves the bundle structure, means that C*-bundle dynamical systems are relativistic systems. We describe a 2-category to unify Einstein's two uses of the phrase general covariance, give concrete examples and construct a generally covariant quantum system. Motivations include the point of view of virtual points hiding in fibres of a C*-bundle over $X$ and that physical geometry is instrinsically non-local.

9 pages. (Notes) other papers: http://arxiv.org/a/martins_r_2

References in corpus (4)

• What is the Mathematical Structure of Quantum Spacetime?
• C*-bundle dynamical systems
• Model Categories and Quantum Gravity
• Spectral C*-categories and Fell bundles with path-lifting