For the description of observables and states of a quantum system, it may be convenient to use a canonical Weyl algebra of which only a subalgebra A, with a non-trivial center Z , describes observables, the other Weyl operators playing the role of intertwiners between inequivalent representations ofA. In particular, this gives rise to a gauge symmetry described by the action of Z . A distinguis...

We give relations between main operators of quantum mechanics on one of most general classes of nilpotent Lie groups. Namely, we show relations between momentum and position operators as well as Euler and Coulomb potential operators on homogeneous groups. Homogeneous group analogues of some well-known inequalities such as Hardy's inequality, Heisenberg-Kennard type and Heisenberg-Pauli-Weyl typ...

We study the propagation of gravitational waves carrying arbitrary information through isotropic cosmologies. The waves are modelled as small perturbations of the background Robertson–Walker geometry. The perfect fluid matter distribution of the isotropic background is, in general, modified by small anisotropic stresses. For pure gravity waves, in which the perturbed Weyl tensor is radiative (i...

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 having a cyclic and diffeomorphism invariant vector, is already unitarily equivalent to the fundamental representation. Additional assumptions concern the dimen...

We are interested in remainder estimates in the Weyl formula for the asymptotic number of eigenvalues of certain elliptic operators on R and on a smooth compact manifold without boundary. The main aim of this paper is to compare spectral asymptotics of operators with irregular coefficients and certain classes of smoothed operators for which the Weyl formula is derived by means of elementary pse...

We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general covariance. Up to a constant, the anomaly only depends on the dimension d of the manifold on which the conformal field theory is defined. We present concrete ...

Let X be a complex manifold with strongly pseudoconvex boundary M . If ψ is a defining function for M , then − logψ is plurisubharmonic on a neighborhood of M in X, and the (real) 2-form σ = i∂∂(− logψ) is a symplectic structure on the complement of M in a neighborhood in X of M ; it blows up along M . The Poisson structure obtained by inverting σ extends smoothly across M and determines a cont...

For a positive integer c, letHc be the subgroup of G obtained when x, y, cz are integers. The Heisenberg manifold Mc is the quotient G/Hc. Nonzero Poisson brackets on Mc invariant under left translation by G are parametrized by two real parameters μ, ν with μ + ν 6= 0 [4]. For each positive integer c and real numbers μ, ν Rieffel constructed a C*-algebra A μ,ν , quantum Heisenberg manifold (QHM...

Since the fundamental work of Bayen et al. [1] in the seventies, a lot of effort has been dedicated to show the existence of deformations of a Poisson manifold. Some landmarks in this way were the proof of the existence of differential star products for symplectic manifolds which was done independently by De Wilde and Lecomte [2] and Fedosov [5], using different constructions. It turned out tha...

A coordinate-free definition for Wick-type symbols is given for symplectic manifolds by means of the Fedosov procedure. The main ingredient of this approach is a bilinear symmetric form defined on the complexified tangent bundle of the symplectic manifold and subject to some set of algebraic and differential conditions. It is precisely the structure which describes a deviation of the Wick-type ...