The phase space S ×Z for a particle on a circle is considered. Displacement operators in this phase space are introduced and their properties are studied. Wigner and Weyl functions in this context are also considered and their physical interpretation and properties are discussed. All results are compared and contrasted with the corresponding ones for the harmonic oscillator in the R × R phase s...

We investigate a class of algebras that provides multiparameter versions of both quantum symplectic space and quantum Euclidean 2n-space. These algebras encompass the graded quantized Weyl algebras, the quantized Heisenberg space, and a class of algebras introduced by Oh. We describe the structure of the prime and primitive ideals of these algebras. Other structural results include normal separ...

We study the evolution of the Weyl curvature invariant in all spatially homogeneous universe models containing a non-tilted γ-law perfect fluid. We investigate all the Bianchi and Thurston type universe models and calculate the asymptotic evolution of Weyl curvature invariant for generic solutions to the Einstein field equations. The influence of compact topology on Bianchi types with hyperboli...

Causal structure, inertial path structure and compatibility with quantum mechanics demand no full Lorentz metric, but only an integrable Weyl geometry for space time (Ehlers/Pirani/Schild 1972, Audretsch e.a. 1984). A proposal of (Tann 1998, Drechsler/Tann 1999) for a minimal coupling of the Hilbert-Einstein action to a scale covariant scalar vacuum field φ (weight −1) plus (among others) a Kle...

In this paper we elaborate on the structure of the continuous-time histories description of quantum theory, which stems from the consistent histories scheme. In particular, we examine the construction of history Hilbert space, the identification of history observables and the form of the decoherence functional (the object that contains the probability information). It is shown how the latter is...

We study the isometric spacelike embedding problem in scaled de Sitter space, and obtain Weyl-type estimates corresponding closedness space of embeddings.

Symplectic reduction, also known as Marsden-Weinstein reduction, is an important construction in Poisson geometry. Following N.P. Landsman [22], we propose a quantization of this procedure by means of M. Rieffel’s theory of induced representations. Here to an equivariant momentum map there corresponds an operator-valued rigged inner product. We define the operatoralgebraic notions that are invo...