40 research outputs found
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 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 algebra of the noncommutative
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 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 we investigate
different U(1) instanton solutions tied by isometry trasformations. These
solutions present a form of vector fields in noncommutative
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.