All fiber bundles with a given set of characteristic classes can be considered as particular projections more general bundle called universal classifying space. This notion projector valued field, global definition connections and gauge fields, may useful in defining vector for noncommutative base spaces. In this letter we derive the field fuzzy sphere, define n-monopole configurations, check that classical limit, using machinery geometry, corresponding topological charges (Chern class) are integers.

We search a canonical basis of Dirac's observables for the classical Abelian Higgs model with fermions in case trivial U(1) principal bundle. The study Gauss law first class constraint shows that has two disjoint sectors solutions associated physically different phases. In electromagnetic phase, field remains massless: after determination we get both reduced physical Hamiltonian and Lagrangian are nonlocal. becomes massive terms local, but nonanalytic electric charge (or equivalently sum...

We consider a matrix model depending on the parameter λ which permits fuzzy sphere as classical background. By expanding bosonic matrices around this background one recovers U(1) (U(n)) noncommutative gauge theory sphere. To check stability of background, we look for new solutions and find them < 1, that make solution unstable [Formula: see text] stable otherwise.

In this paper we shall investigate the possibility of solving U(1) theories on non-commutative (NC) plane for arbitrary values θ by exploiting Morita equivalence. This duality maps NC two-torus with a rational parameter to standard U(N) theory in presence 't Hooft flux, whose solution is completely known. Thus, assuming smooth dependence θ, are able construct series approximants original theory, which finally reached taking large-N limit at fixed flux. As see, procedure hides some...

We search a canonical basis of Dirac's observables for the classical non-Abelian Higgs model with fermions in case trivial SU(2) principal bundle complex doublet fields and given representation SU(2). Since each one three Gauss law first class constraints can be solved either corresponding longitudinal electric field or momentum, we get priori eight disjoint phases solutions model. The only two covariance are phase massless massive fields. Dirac reduced physical (local) Hamiltonian...

The classical dynamics of some vortex models coupled to gravity in the critical coupling is considered. We derive set Bogomol’nyi-type equations motion for Abelian Higgs model and Chern-Simons model, gravity. In both cases we are able reduce a single nonlinear equation which generalizes, on curved space, corresponding plane. finally compute asymptotic behavior multivortex configuration from N particle metric without with spin, respectively.

We show that the algebraic method solving ordinary harmonic oscillator can be adapted to non-commutative case.

The complete, missing, Hamiltonian treatment of the standard SU(3)xSU(2)xU(1) model with Grassmann-valued fermion fields in Higgs phase is given. We bypass complications theory phase, resulting from spontaneous symmetry breaking mechanism, by studying formulation for gauge equivalent Lagrangian unitary gauge. A canonical basis Dirac's observables found and reduced physical evaluated. Its self-energy part nonlocal electromagnetic strong interactions, but local weak ones. Therefore, Fermi...

We show that this problem gives rise to the same differential equation of a well known potential ordinary quantum mechanics. However there is subtle difference in choice parameters hypergeometric function solving which changes physical discussion spectrum.

We show how to modify the canonical transformations make them compatible with non-commutative Poisson brackets.

We describe how to reduce the fuzzy four-sphere algebra a set of four independent raising and lowering oscillator operators. In terms them we derive projector valued operators for four-sphere, which are global definition k-instanton connections over this noncommutative base manifold.

We propose an action for gravity on a fuzzy sphere, based matrix model. find striking similarities with analogous model of two-dimensional noncommutative plane, i.e. the solution space both models is spanned by pure U(2) gauge transformations acting background model, and there exist deformations classical diffeomorphisms which preserve actions.

We study the interconnection between finite projective modules for a fuzzy sphere, determined in previous paper, and matrix model approach, making clear physical meaning of noncommutative topological configurations.

We find that in presence of noncommutative Poisson brackets, the relation between Lagrangian and Hamiltonian is modified. discuss this property by using path integral formalism for non-relativistic systems. apply procedure to harmonic oscillator with a minimal length.

We deconstruct the finite projective modules for fuzzy four-sphere, described in a previous paper, and correlate them with matrix model approach, making manifest physical implications of noncommutative topology. briefly discuss also U(2) case, being smooth deformation celebrated BPST SU(2) classical instantons on sphere.