相关论文: AQV II. A new formulation of the Weyl C*-algebra
In this article a new C*-algebra derived from the basic quantum variables: holonomies along paths and group-valued quantum flux operators in the framework of Loop Quantum Gravity is constructed. This development is based on the theory of…
The Weyl algebra A of continuous functions and exponentiated fluxes, introduced by Ashtekar, Lewandowski and others, in quantum geometry is studied. It is shown that, in the piecewise analytic category, every regular representation of A…
In this article the holonomy-flux *-algebra, which has been introduced by Lewandowski, Okolow, Sahlmann and Thiemann, is modificated. The new *-algebra is called the holonomy-flux cross-product *-algebra. This algebra is an abstract…
In the theory of C*-algebras, the Weyl groups were defined for the Cuntz algebras and graph algebras by Cuntz and Conti et al. respectively. In this paper, we introduce and investigate the Weyl groups of groupoid C*-algebras as a natural…
We introduce the holonomy-diffeomorphism algebra, a C*-algebra generated by flows of vectorfields and the compactly supported smooth functions on a manifold. We show that the separable representations of the holonomy-diffeomorphism algebra…
The standard C*-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does…
In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain an ambient category in which we determine subcategories…
Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic…
We study multivariate generalisations of the classical Wiener--Hopf algebra, which is the C$^*$-algebra generated by the Wiener--Hopf operators, given by the convolutions restricted to convex cones. By the work of Muhly and Renault, this…
A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a…
We continue an analysis of representations of cylindrical functions and fluxes which are commonly used as elementary variables of Loop Quantum Gravity. We consider an arbitrary principal bundle of a compact connected structure group and…
S. L. Woronowicz's theory of introducing C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators…
Recently, we have constructed a non{linear (polynomial) extension of the 1-mode Heisenberg group and the corresponding Fock and Weyl representations. The transition from the 1-mode case to the current algebra level, in which the operators…
We study multivariate generalisations of the classical Wiener--Hopf algebra, which is the C$^*$-algebra generated by the Wiener--Hopf operators, given by the convolutions restricted to convex cones. By the work of Muhly and Renault, this…
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…
We consider two Z/2Z-actions on the Podles generic quantum spheres. They yield, as noncommutative quotient spaces, the Klimek-Lesniewski q-disc and the quantum real projective space, respectively. The C*-algebras of all these quantum spaces…
Integral calculus on the space of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of diffeomorphism invariant theories of…
Any deformation of a Weyl or Clifford algebra can be realized through a change of generators in the undeformed algebra. q-Deformations of Weyl or Clifford algebrae that were covariant under the action of a simple Lie algebra g are…
We study a quantum (non-commutative) representation of the affine Weyl group mainly of type $E_8^{(1)}$, where the representation is given by birational actions on two variables $x$, $y$ with $q$-commutation relations. Using the tau…
We introduce $C^*$-algebras associated with directed graphs, along with two generalizations of this concept, namely Exel-Pardo $C^*$-algebras associated with a self-similar action of a group on a directed graph, and the $C^*$-algebras…