Weyl covariant theories of gravity in 3-dimensional Riemann–Cartan–Weyl space-times

Gravity and Einstein-Proca-Weyl theories extended to a class of Scalar gravity theories

We extend the recently proved relation between certain models of Non-Riemannian gravitation and Einstein-Proca-Weyl theories to a class of Scalar gravity theories, this is used to present a Black-Hole Dilaton solution with non-Riemannian connection. PACS numbers: 04.20J, 0450, 0425.Dm, 04.40.Nr, 0470-s permanent address, e-mail: [email protected]

On Weyl-covariant channels

Formalism of discrete noncommutative Fourier transform is developed and applied to the study of Weyl-covariant channels. We then extend a result in [6] concerning a bound of the maximal output 2-norm of a Weyl-covariant channel. A class of channels which attain the bound is introduced, for which the multiplicativity of the maximal output 2-norm is proven. Complementary channels are described wh...

Five-Dimensional Space-Times

A Weyl-covariant tensor calculus

On a (pseudo-) Riemannian manifold of dimension n > 3, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called generalized connections and their transformation laws under diffeomorphisms and Weyl r...

Hilbert space structure of covariant loop quantum gravity

We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum states are realized by a generalization of spin network states based on Lorentz Wilson lines projected on irreducible representations of an SO(3) subgroup. The pr...