The Quantum Spheres and their Embedding into Quantum Minkowski Space-Time

We recast the Podle\`s spheres in the noncommutative physics context by showing that they can be regarded as slices along the time coordinate of the different regions of the quantum Minkowski space-time. The investigation of the transformations of the quantum sphere states under the left coaction of the ${\cal SO}_{q}(3)$ group leads to a decomposition of the transformed Hilbert space states in terms of orthogonal subspaces exhibiting the periodicity of the quantum sphere states

On the ADHM construction of noncommutative U(2) k-instanton

The basic objects of the ADHM construction are reformulated in terms of elements of the $A_{\theta}(R^4)$ algebra of the noncommutative $R_{\theta}^4$ space. This new formulation of the ADHM construction makes possible the explicit calculus of the U(2) instanton number which is shown to be the product of a trace of finite rank projector of the Fock representation space of the algebra $A_{\theta}(R^4)$ times a noncommutative version of the winding number.Comment: 22 pages, new version to appear in Phys. Rev.

On the Generalized Einstein-Cartan Action with Fermions

From the freedom exhibited by the generalized Einstein action proposed in [1], we show that we can construct the standard effective Einstein-Cartan action coupled to the fermionic matter without the usual current-current interaction and therefore an effective action which does not depend neither on the Immirzi parameter nor on the torsion. This establishes the equivalence between the Einstein-Cartan theory and the theory of the general relativity minimally coupled to the fermionic matter.Comment: 8 pages, Added references, Corrected typos, Accepted in Class. Quant. Gra

On the Quantum Lorentz Group

The quantum analogues of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indiceswe construct a quantum Minkowsky metric. In this framework, we show explicitely the correspondance between the SL(2,C) and Lorentz quantum groups.Comment: 17 page

The flux of noncommutative U(1) instanton through the fuzzy spheres

From the ADHM construction on noncommutative $R_{\theta}^4$ we investigate different U(1) instanton solutions tied by isometry trasformations. These solutions present a form of vector fields in noncommutative $R_{\theta}^3$ vector space which makes possible the calculus of their fluxes through fuzzy spheres. We establish the noncommutative analog of Gauss theorem from which we show that the flux of the U(1) instantons through fuzzy spheres does not depend on the radius of these spheres and it is invariant under isometry transformations.Comment: 18 pages, new version to appear in Int. Jour. of Mod. Phys.