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...

let $(m^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the sasakian space form$widetilde{m}(c)$. we show that if the shape operator $a$ of $m$ isrecurrent then it is parallel. moreover, we show that $m$is locally a product of two constant $phi-$sectional curvaturespaces.

We calculate the integrated trace anomaly for a real spin-0 scalar field in six dimensions in a torsionless curved space without a boundary. We use a path integral approach for a corresponding supersymmetric quantum mechanical model. Weyl ordering the corresponding Hamiltonian in phase space, an extra two-loop counterterm 1 8 (

Canonical transformations are studied in the bosonic Fock space using coherent and ultracoherent vectors. The connection between the Weyl operator and the homogeneous canonical transformations (Bogoliubov transformations) is presented. The unitary ray representation of the symplectic group is defined in the bosonic Fock space by the action of the group on the ultracoherent vectors.