We describe the construction of non-commutative manifolds, which are the non-commutative analogs of homogeneous spaces using coherent states. In the commutative limit we obtain standard manifolds. Applications to the Fuzzy sphere and to the Fuzzy hyperboloid are discussed in more detail. *) Part of Project Nr. P8916-PHY of the \Fonds zur FF orderung der wissenschaftlichen Forschung in Osterreich".

We notice that, for branes wrapped on complex analytic subvarieties, the algebraic-geometric version of K-theory makes the identification between brane-antibrane pairs and lower-dimensional branes automatic. This is because coherent sheaves on the ambient variety represent gauge bundles on subvarieties, and they can be put in exact sequences (pro-jective resolutions) with sheaves corresponding ...

The time evolution of even and odd squeezed states, as well as that of squeezed number states, has been given in simple, analytic form. This follows experimental work on trapped ions which has demonstrated even and odd coherent states, number states, and squeezed (but not displaced) ground states. We review this situation and consider the extension to even and odd squeezed number states. Questi...

Representations of the superalgebra osp(2|2) and current superalgebra osp(2|2) (1) k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2|2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2|2) (1) k in the standard basis are obtained for arbitrary level k.

In this paper we consider moduli spaces of coherent systems on an elliptic curve. We compute their Hodge polynomials and determine their birational types in some cases. Moreover we prove that certain moduli spaces of coherent systems are isomorphic. This last result uses the Fourier-Mukai transform of coherent systems introduced by Hernández Ruiperez and Tejero Prieto.

A detailed and rigorous analysis of Gödel’s proof of his first incompleteness theorem is presented. The purpose of this analysis is two-fold. The first is to reveal what Gödel actually proved to provide a clear and solid foundation upon which to base future research. The second is to construct a coherent explication of Gödel’s proof that is not only approachable by the non-specialist, but also ...