Noncommutativity due to spin

Using the Berezin-Marinov pseudoclassical formulation of spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular momentum. The quantization of the model leads to the noncommutativity with mixed spacial and spin degrees of freedom. A modified Pauli equation, describing a spin half particle in an external e.m. field is obtained. We show that nonlocality caused by the spin noncommutativity depends on the spin of the particle; for spin zero, nonlocality does not appear, for spin half, $\Delta x\Delta y\geq\theta^{2}/2$, etc. In the relativistic case the noncommutative Dirac equation was derived. For that we introduce a new star product. The advantage of our model is that in spite of the presence of noncommutativity and nonlocality, it is Lorentz invariant. Also, in the quasiclassical approximation it gives noncommutativity with a nilpotent parameter.Comment: 11 pages, references adda

Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems

We associate to an arbitrary $\mathbb Z$-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer--Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given.Comment: LaTeX2e, 18 page

The Noncommutative Supersymmetric Nonlinear Sigma Model

We show that the noncommutativity of space-time destroys the renormalizability of the 1/N expansion of the O(N) Gross-Neveu model. A similar statement holds for the noncommutative nonlinear sigma model. However, we show that, up to the subleading order in 1/N expansion, the noncommutative supersymmetric O(N) nonlinear sigma model becomes renormalizable in D=3. We also show that dynamical mass generation is restored and there is no catastrophic UV/IR mixing. Unlike the commutative case, we find that the Lagrange multiplier fields, which enforce the supersymmetric constraints, are also renormalized. For D=2 the divergence of the four point function of the basic scalar field, which in D=3 is absent, cannot be eliminated by means of a counterterm having the structure of a Moyal product.Comment: 15 pages, 7 figures, revtex, minor modifications in the text, references adde

On the properties of the interstellar medium in extremely metal-poor blue compact dwarf galaxies: GMOS-IFU spectroscopy and SDSS photometry of the double-knot galaxy HS 2236+1344

The main goal of this study is to carry out a spatially resolved investigation of the warm interstellar medium (ISM) in the extremely metal-poor Blue Compact Dwarf (BCD) galaxy HS 2236+1344. Special emphasis is laid on the analysis of the spatial distribution of chemical abundances, emission-line ratios and kinematics of the ISM, and to the recent star-forming activity in this galaxy. This study is based on optical integral field unit spectroscopy data from Gemini Multi-Object Spectrograph at the Gemini North telescope and archival Sloan Digital Sky Survey images. The data were obtained in two different positions across the galaxy, obtaining a total 4 arcsec X 8 arcsec field which encompasses most of its ISM. Emission-line maps and broad-band images obtained in this study indicate that HS 2236+1344 hosts three Giant HII regions. Our data also reveal some faint curved features in the BCD periphery that might be due to tidal perturbations or expanding ionized-gas shells. The ISM velocity field shows systematic gradients along the major axis of the BCD, with its south-eastern and north-western half differing by ~80 km/s in their recessional velocity. The Ha and Hb equivalent width distribution in the central part of HS 2236+1344 is consistent with a very young (~3 Myr) burst. Our surface photometry analysis indicates that the ongoing starburst provides ~50% of the total optical emission, similar to other BCDs. It also reveals an underlying lower-surface brightness component with moderately red colors, which suggest that the galaxy has undergone previous star formation. We derive an integrated oxygen abundance of 12+log(O/H)=7.53\pm0.06 and a nitrogen-to-oxygen ratio of log(N/O)=-1.57\pm0.19. Our results are consistent, within the uncertainties, with a homogeneous distribution of oxygen and nitrogen within the ISM of the galaxy. (abridged)Comment: 15 pages, 16 figures, accepted for publication in A&

The 1/N Expansion in Noncommutative Quantum Mechanics

We study the 1/N expansion in noncommutative quantum mechanics for the anharmonic and Coulombian potentials. The expansion for the anharmonic oscillator presented good convergence properties, but for the Coulombian potential, we found a divergent large N expansion when using the usual noncommutative generalization of the potential. We proposed a modified version of the noncommutative Coulombian potential which provides a well-behaved 1/N expansion.Comment: v2: resided version, to appear in PRD, 18 pages, 4 figure