Related papers: Applications to quantum gravity from C*-bundles

Consistent and covariant Lorentz and diffeomorphism anomalies are investigated in terms of the geometry of the universal bundle for gravity. This bundle is explicitly constructed and its geometrical structure will be studied. By means of…

We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calculation of the vacuum energy of spacetime curvature…

This work is concerned with the notion of {eigenstates} for $C^*$-algebras. After reviewing some basic and structural results, we explore the possibility of reinterpreting certain typical concepts of quantum mechanics (\eg dynamical…

Given a compact space X and two commuting continuous open surjective maps sigma_1, sigma_2 : X --> X, we construct certain C*-algebras that reflect the dynamics of the N^2-action. When the maps sigma_1, sigma_2 are local homeomorphisms,…

We study the $C^*$-algebras associated to upper-semicontinuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer--Raeburn "Stabilization Trick," we construct from each such bundle a groupoid…

We study $C^*$-algebras arising from $C^*$-correspondences, which was introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our $C^*$-algebras to be nuclear, exact, or satisfy the Universal…

`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…

We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…

This is a book about Partial Actions and Fell Bundles with applications to C*-algebras generated by partial isometries. Here is the table of contents: 1-Introduction, 2-Partial actions, 3-Restriction and globalization, 4-Inverse semigroups,…

We recall the emergence of a generalized gauge theory from a noncommutative Riemannian spin manifold, viz. a real spectral triple $(A,H,D;J)$. This includes a gauge group determined by the unitaries in the $*$-algebra $A$ and gauge fields…

We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in the framework of compact quantum group theory and…

Based on a fact that complex Clifford algebras of even dimension are isomorphic to the matrix ones, we consider bundles in Clifford algebras whose structure group is a general linear group acting on a Clifford algebra by left…

It is shown how a C*-algebra representation of the transformations of a physical system can be derived from two operational postulates: 1) the existence of dynamically independent systems}; 2) the existence of symmetric faithful states.…

In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some…

A $C^*$-textile dynamical system $({\cal A}, \rho,\eta,\Sigma^\rho,\Sigma^\eta, \kappa)$ connsists of a unital $C^*$-algebra ${\cal A}$, two families of endomorphisms ${\rho_\alpha}_{\alpha \in \Sigma^\rho}$ and ${\eta_a}_{a \in…

This survey article is concerned with the modeling of the kinematical structure of quantum systems in an algebraic framework which eliminates certain conceptual and computational difficulties of the conventional approaches. Relying on the…

In this work we construct a C*-algebra from an injective endomorphisms of some group G, allowing the endomorphism to have infinite cokernel. We generalize results obtained by I. Hirshberg and also by J. Cuntz and A. Vershik. In good cases…

An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…

In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a…

The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until…