On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space

We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras $sl(2,\mathbb{R})$ or $su(2)$ according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential. PACS: 03.65.-w; 03.65.Fd MSC: 81R05; 20C35; 22E70Comment: 49 pages. No figures. Version to appear in JP

Pade-related resummations of the pressure of quark-gluon plasma by approximate inclusion of g**6-terms

We perform various resummations of the hot QCD pressure based on the actual knowledge of the perturbation series which includes the g**6 ln(1/g) and part of the g**6 terms. Resummations are performed separately for the short- and long-distance parts. The g**6 term of the short-distance pressure is estimated on the basis on the known UV cutoff dependence of the long-distance part. The resummations are of the Pade and Borel-Pade type, using in addition the (Pade-)resummed expression for the squared screening mass mE**2 and for the EQCD coupling parameter gE**2. The resummed results depend weakly on the yet unknown g**6 terms and on the the short-range renormalization scale, at all temperatures. The dependence on the long-range renormalization scale is appreciable at low temperatures T < 1 GeV. The resulting dependence of pressure on temperature T is compatible with the results of the lattice calculations at low T.Comment: 25 pages, 15 double figures, 4 single figures, revtex4; thoroughly extended analysis; more figures; conclusions more clearly formulated; new references added; title slightly changed; accepted for publication in Phys.Rev.

The Landau problem and noncommutative quantum mechanics

The conditions under which noncommutative quantum mechanics and the Landau problem are equivalent theories is explored. If the potential in noncommutative quantum mechanics is chosen as $V= \Omega \aleph$ with $\aleph$ defined in the text, then for the value ${\tilde \theta} = 0.22 \times 10^{-11} cm^2$ (that measures the noncommutative effects of the space), the Landau problem and noncommutative quantum mechanics are equivalent theories in the lowest Landau level. For other systems one can find differents values for ${\tilde \theta}$ and, therefore, the possible bounds for ${\tilde \theta}$ should be searched in a physical independent scenario. This last fact could explain the differents bounds for $\tilde \theta$ found in the literature.Comment: This a rewritten and corrected version of our previous preprint hep-th/010517

Chiral Condensates in Quark and nuclear Matter

We present a novel treatment for calculating the in-medium quark condensates. The advantage of this approach is that one does not need to make further assumptions on the derivatives of model parameters with respect to the quark current mass. The normally accepted model-independent result in nuclear matter is naturally reproduced. The change of the quark condensate induced by interactions depends on the incompressibility of nuclear matter. When it is greater than 260 MeV, the density at which the condensate vanishes is higher than that from the linear extrapolation. For the chiral condensate in quark matter, a similar model-independent linear behavior is found at lower densities, which means that the decreasing speed of the condensate in quark matter is merely half of that in nuclear matter if the pion-nucleon sigma commutator is six times the average current mass of u and d quarks. The modification due to QCD-like interactions is found to slow the decreasing speed of the condensate, compared with the linear extrapolation.Comment: 12 pages, 7 figures, revtex4 styl

QED vacuum fluctuations and induced electric dipole moment of the neutron

Quantum fluctuations in the QED vacuum generate non-linear effects, such as peculiar induced electromagnetic fields. In particular, we show here that an electrically neutral particle, possessing a magnetic dipole moment, develops an induced electric dipole-type moment with unusual angular dependence, when immersed in a quasistatic, constant external electric field. The calculation of this effect is done in the framework of the Euler-Heisenberg effective QED Lagrangian, corresponding to the weak field asymptotic expansion of the effective action to one-loop order. It is argued that the neutron might be a good candidate to probe this signal of non-linearity in QED.Comment: A misprint has been corrected, and three new references have been adde

Observability of an induced electric dipole moment of the neutron from nonlinear QED

It has been shown recently that a neutron placed in an external quasistatic electric field develops an induced electric dipole moment $\mathbf{p}_{\mathrm{IND}}$ due to quantum fluctuations in the QED vacuum. A feasible experiment which could detect such an effect is proposed and described here. It is shown that the peculiar angular dependence of $\mathbf{p}_{\mathrm{IND}}$ on the orientation of the neutron spin leads to a characteristic asymmetry in polarized neutron scattering by heavy nuclei. This asymmetry can be of the order of $10^{-3}$ for neutrons with epithermal energies. For thermalized neutrons from a hot moderator one still expects experimentally accessible values of the order of $10^{-4}$. The contribution of the induced effect to the neutron scattering length is expected to be only one order of magnitude smaller than that due to the neutron polarizability from its quark substructure. The experimental observation of this scattering asymmetry would be the first ever signal of nonlinearity in electrodynamics due to quantum fluctuations in the QED vacuum

Pion form factor in the Kroll-Lee-Zumino model

The renormalizable Abelian quantum field theory model of Kroll, Lee, and Zumino is used to compute the one-loop vertex corrections to the tree-level, Vector Meson Dominance (VMD) pion form factor. These corrections, together with the known one-loop vacuum polarization contribution, lead to a substantial improvement over VMD. The resulting pion form factor in the space-like region is in excellent agreement with data in the whole range of accessible momentum transfers. The time-like form factor, known to reproduce the Gounaris-Sakurai formula at and near the rho-meson peak, is unaffected by the vertex correction at order $\cal{O}$(g_\rpp^2).Comment: Revised version corrects a misprint in Eq.(1

Field of homogeneous Plane in Quantum Electrodynamics

We study quantum electrodynamics coupled to the matter field on singular background, which we call defect. For defect on the infinite plane we calculated the fermion propagator and mean electromagnetic field. We show that at large distances from the defect plane, the electromagnetic field is constant what is in agreement with the classical results. The quantum corrections determining the field near the plane are calculated in the leading order of perturbation theory.Comment: 16 page

Massless fermions in a bag at finite density and temperature

We introduce the chemical potential in a system of massless fermions in a bag by impossing boundary conditions in the Euclidean time direction. We express the fermionic mean number in terms of a functional trace involving the Green's function of the boundary value problem, which we study analytically. Numerical evaluations are made, and an application to a simple hadron model is discussed.Comment: 14 pages, 3 figures, RevTe